Solved: a. List the sample space in the given experiment. How many outcomes possible? b. Construct a table showing the number of defective computers in each outcome and assign this number to this outcome. What is the value of the random variable X? c. Illustrate a probability distribution. What is the probability value PIX) each value of the random variable? d. What is the sum of the probabilities of all values of the random variable? e. What do you notice about the probability of each value of the random variable? to

Two balls are drawn in succession without replacement from an urn containing 9 yellow balls and 6 green balls. Let X X be the random variable representing the number of yellow balls. Question: How many possible outcomes are there in…

Twenty samples each of size 10 were inspected. The number of defectives detected in each of them is given below: 0, 1, 0, 3, 9, 2, 0, 7, 0, , 1, 0, 0, 3, 1, 0, 0, 2, 1, 0 Find the control limits for the number of defectives …

2. A roulette wheel is divided into 25 sectors of equal area numbered from 1 to 25. Find a formula for the probability distribution of X, the number that occurs when the wheel is spun

A laboratory supervision in Type III hospital is investigating a number of reported on-the-job training accidents related to needle stick injuries over a period of one month. Based on the past records, she has the following records on…

Construct the probability distribution for each random variable X. a. The random variable X represents the number of heads that occur when you toss 4 coins at the same time. b. The random variable X represents the number of …

Which of the following looks most like an F distribution? 1. T distribution. 2. F distribution 3. Normal distribution. 4. Another one.

The salary distribution ('000) of 1000 employees at a certain company is as follows: Salary (years) frequency 25-39 20 40-49 32 50-59 30 60-64 10 65-69 8 a, Construct the bar-chart of the data b, Construct the histogram of…

Consider estimating the mean of a variable drawn from a population with mean u and standard deviation o, using the following formulae: Ĥ1 = x1. X + x2 2 X1 + 2x2 X +x2 3 is = %3D Assume that in all cases the individual estimates x, ar…

Let Xl, "', X" be a random sample from the density where - B < thetha < B f(x; U) = e-(x-B) exp (_e-(X-B)), (a) Find a method-of-moments estimator of B. (b) Find a maximum-likelihood estimator of B

The lifetime of a light bulb is normally distributed with 800 hours and standard deviation 50 hours. A random light bulb is selected. What is the probability that it will last for more than 950 hours?

Stacy de Leon, a physics major, is a prolific writer and a math genius of this university. If it is known that Stacy's IQ belongs to the upper 1% of the learner population, what is her minimum IQ?

X = [0.01, 0.36, 0.97, 0.44, 0.86, 0.49, 0.02, 0.19, 0.54, 0.63, 0.69, 0.27, 0.21, 0.55, 0.54, 0.1 , 0.02, 0.49 , 0.42, 0.79], is a list of 20 random numbers generated from a pseudo-random number generator G. a. What is a uniformit…

There are three grades in a report card that you want to interpret in terms of performance: mathematics 75, english 85, and science 90. This means are 72,83 and 88, respectively. The standard deviation are 3, 10, and 15, respectively

In a class of 28 students, 16 play an instrument and 11 play a sport. There are 7 students who do not play an instrument or a sport. What is the probability that a student plays an instrument given that they play a sport?

If all of your computer data are stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that both drives will fail during a year?

In a class of 28 students, 16 play an instrument and 11 play a sport. There are 7 students who do not play an instrument or a sport. What is the probability that a student plays an instrument given that they play a sport?

In a railway yard goods trains arrive that at the rate of 30 trains per day. Assuming that the inter-arrival time follows an exponential distribution and the service time distribution is also exponential with an average of 36 mi…

1. Consider the random quantity X, with PDF fx(x) = {4/3(2x-x^2), 0

A shipment of five computers contains two that slightly defective. If a retailer receives three of these computers at random, list the elements of the sample space S using the letters D and N for defective and non-defective compute…

1. Each sample of water has a 10% chance of containing a particular organic pollutant. Assume that the samples are independent with regard to the presence of the pollutant. Let X =the number of samples that contain the pollutant in…

Construct a probability distribution for the data and draw a histogram for the following: The probabilities that a patient will have 0,1 ,2 , or 3 medical tests performed on entering a hospital are 6/15, 5/15, 3/15, and 1/15 respec…

1. The number of calls coming into a hotel’s reservation center averages three per minute. a. Find the probability that no calls will arrive in a given one-minute period. b. Find the probability that at least two calls will arrive…

The probability that aa new automobile has a backup camera is 0.6. The probability that a new automobile has a GPS system is 0.4. The probability that a new automobile has both a backup camera and GPS is 0.2. If a new automo…

1. The manufacturer of a certain kind of light bulb claims that the lifetime of the bulb in hours, X can be modeled as a random quantity with PDF. fx(x)= {0, x<100 c/x2, x>=100, where c is a constant. i. What…

Nine out of every 100 people in the Philippines have Type B positive blood. If 8 people are chosen at random, what is the probability that less than 3 people have Type B blood?

An achievement research was conducted to the Grade 10 students of Scott National High School. The researcher randomly selected twenty (20) Grade 10 students to take a diagnostic exam in Mathematics at the start of the school year. The…

A mean of 3 out of 5 students request for tomato sauce with their meal in a canteen. A random sample of 8 students is selected, what is the probability that less than 4 students request for tomato sauce with their meal?

In a study of the effects of early Alzheimer’s disease on nondeclarative memory, the Category Fluency Test to establish baseline persistence and semantic memory and language abilities. The eight subjects in the sample had Category Flu…

A researcher thinks that people under the age of twenty have vocabularies that are different than those of people over sixty years of age. Thus, to test this hypothesis, the researcher administers a vocabulary test to a group of 25 yo…

In the study of urinary tract infection, the sample and proportion in the group of fosfomycin / trometamol was 25, 0.92 and trimethoprim / sulfamethoxazole was 16, 0.61, respectively. a) Find the difference in proportions. (0.5) 4…

Use the normal distribution of heights of adult women, which has a mean of 165 centimeters and a standard deviation of 4 centimeters and the following table with the standard scores and percentiles for a normal distribution to find t…

The lifetime of bulbs produced by Tariqs lightening company follows a normal distribution with a mean of 3462 hours and a standard deviation 1070 hours. What is the probability that randomly selected bulb will have a lifetime of at mo…

If the diameters of ball bearings are normally distributed with mean 0.6140 inches and standard deviation 0.0025 inches, determine the percentage of ball bearings with diameters, (a) between 0.610 and 0.618 inches inclusive (b) greate…

A random of 200 school managers were administered a developed leadership skill test. The sample mean and standard deviation were 78 and 4.2 respectively. In the standardization of test, the mean was 73 and the standard deviation was 8…

A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112.5. Is there sufficient evidence to support the principal’s cl…

& A survey will be conducted on the use of social media among senior high school students. a. How large a sample must be obtained if the researchers want to be 95% confident that the error will not exceed 5%? …

The probability function of a discrete random variable X is as follows: Values of X: x -4 -2 0 2 4 P(x) k 2k 3k 5k 6k i) Find the value of k. ii) Find the probability of the value of X exactly one. iii) Find the probability of …

Four balls are drawn in succession without replacement from an urn containing 4 red balls, 3 blue balls and 3 yellow balls. Let Z be the random variable representing the number of blue balls.

In a betting game wherein the result may be one of the following in one turn: break even, win 5 peso or lose 3 peso. How much will be the amount a player gets after three turns. Let X be the total amount of a player gets after three t…

1.The curve between 0 and -2.0? 2.The curve to the right of 1.5

1. The mean life time of a sample of 16 fluorescent light bulbs produced by a company is computed to be 1570 hours. The population standard deviation is 120 hours. Suppose the hypothesized value for the population mean is 1600 hou…

An experimental study was conducted by a researcher to determine if a new time slot has an effect on the performance of pupils in mathematics. Fifteen randomly selected learners participated in the study. Toward the end of the investi…

A population consists of 500 values with mean 50 and variance 5 find mean and standard error of sampling distribution of means for sample size equal to 20 it sampling is done 1) Without replacement 2) With replacement

(a) The central limit theorem is perhaps the most important result in statistics. State and prove it. (b) The times spent by customers coming to a Kalingalinga Total gas station to fill up can be viewed as independent random variab…

Zaheeda scored 9 goals in 5 netball matches at this rate about how many goals will she score in 10 games?

Sally has 11 pairs of socks in her drawer. Each pair is a different color and design, but they are not together as pairs; they are just in her drawer scattered about. With her left hand, Sally reaches in and picks one sock. a. Wh…

2. An experiment consists of tossing a die and then flipping a coin once if the number on the die is even. If the number on the die is odd, the coin is flipped twice. Using the notation 4H, for example, to denote the outcome that the …

1. Daily sales records for a car dealership show that it will sell 0, 1, 2, or 3 cars, with probabilities as listed: Number of Repairs(X) 0 1 2 3 p(x) 0.5 0.3 0.1 0.1 a. Find the probability distribution …

(a) Suppose that 𝜃̂is an estimator for a parameter 𝜃 and 𝐸[𝜃̂] = 𝑎𝜃 + 𝑏 for some nonzero constant 𝑎 and 𝑏. (i) Determine the biasness of the estimator. (ii) Find a function of 𝜃̂, say 𝜃̂∗ that is an unbiased estimator for 𝜃. (b) Given…

If f(x,y)= { t(3x+y) 0 elsewhere 1

In a state, men have a mean height of 168cm, standard deviation 8cm, and women have a mean height of 160cm, standard deviation of 5cm. In a random sample of 100 married couples, the average height differences between husband and wife …

A population has mean=37 and s.d=2.If the distribution is transformed into a new distribution with mean =100 and s.d=20,what new values will be obtained for each of the following scores:35,36,37,38,39,?

It is known from the records of the city schools that the standard deviation of mathematics test score on the XYZ test is 5. A sample of 200 pupils were taken and it was found that the sample mean score is 75. Previous tests showed th…

A.) First sample has n=3 and M=8. Second sample has n=5 and M=6. What is the weighted mean? B.) First sample has n=10 and M=12. Second sample has n=4 and M=7. What is the weighted mean? Also do you mind showing me the formula how …

Let x be a random variable that denotes the number of passenger in a train station for a given hour. What are the possible values of x

A shipment of 25 similar laptop computers to a retail outlet contains 5 that are defective. If a school makes a random purchase of 3 of these computers, find the probability when the school accidentally purchased 1 defective and 2 are…

A family has four children. If x is a random variable that pertains to the number of female children, what are the possible values of x

A jar contains 5 red marbles, 5 white marbles, and 6 blue marbles. Two marbles are randomly selected from the jar with replacement. Find the following probabilities. Leave your answer as a reduced fraction.

One day, Professor brought a box that contains 6 yellow and 7 green marbles in his class in Statistics and Probability subject. He asked one student to draw three marbles, with replacement, in the box. What is the probability when the…

2) Find the expected value and variance of the number of heads obtained when 2 fair coins are tossed simultaneously. Also find (i) the median and mean deviation from median (ii) quartile deviation of the probability distribution…

Nicole Nelson has come into an inheritance from her grandparents. She is attempting to decide among several investment alternatives. The return after one year is dependent primarily on the interest rate during the next year. The rate …

Raphael’s grades in his statistics classes are as follows: Quizzes: 62, 88, 82 Laboratories: 89, 96 Examinations: 87, 99 a. In this class, quizzes count once, laboratories count twice as much as a quiz, and examinations count three ti…

Combination A bag of contains 4 yellow, 8 red and 3 blue balls. How many ways can 3 balls be selected so that the following conditions are met? a. all balls are yellow b. all balls are red c. There is one ball from each co…

Given 𝑥 ̅ = 62 and s = 8. Find the z-score value that corresponds to each of the following scores up to two decimal places. X=70 X=78 X=82 X=50 X=42

How many grams (to the nearest five) are in nine and three eights of an ounce?

A researcher claims that the average wind speed in a certain city is 8 miles per hour. A sample of 32 days has an average wind speed of 8.2 miles per hour. The standard deviation of the population is 0.6 mile per hour. At α = 0.05, is…

A survey found that the average hotel room rate in New Orleans is $88.42 and the average room rate in Phoenix is $80.61. Assume that the data were obtained from two samples of 50 hotels each and that the standard deviations of the pop…

The result of nationwide aptitude test in mathematics are normally distributed with m=80 and s= 15 what is the percentile rank of a score of 84

construct the probability histogram

A card is drawn from a deck of 20 cards (all the cards numbered 1 to 5 in a standard check) and the random variable W gives the number on the card. Construct the probability mass function and its corresponding histogram.

1. A school organized a fundraising activity for its donations to victims of a recent typhoon. It involves selling 1000 raffle tickets. One ticket costs $100. The lone winner of this raffle will receive free tuition worth $30,00. What…

9 boys and 2 girls are to be placed next to each other in the school ground for morning assembly. What is the probability that there are exactly 4 boys between the 2 girls?

The chance that a student will clear the quiz-1 paper is 0.59 and the chance that he will clear both quiz-1 and quiz-2 papers is 0.17. The chance that he will clear at least one quiz paper is 0.74. What is the chance that he will clea…

Pramod goes to a shop to buy some clothes. Shopkeeper shows him 5 shirts, 6 pants and 13 t-shirts. If he selects three clothes at random, then find the probability that, randomly chosen clothes does not contain pant.

1. A school organized a fundraising activity for its donations to victims of a recent typhoon. It involves selling 1000 raffle tickets. One ticket costs $100. The lone winner of this raffle will receive free tuition worth $30,00. What…

There are a total of 180 students who are part of badminton, table tennis and tennis team of the college. Of which 70% of students play table tennis, 10% play tennis and 60% play badminton. It is also noticed that all students who pla…

A person predicts daily whether the price of stocks of wrist watch companies will go up or down. If his prediction on stock price of Titan is correct 4 times out of 8, for Rolex it is correct 2 times out of 4 and for Fossil it is corr…

In a Multiple Select Question, there are 5 options of which one or more can be correct. Let us define an event E that the option ‘A’ is correct. What is the cardinality of E?

The probability of getting a sum divisible by three if a pair of fair dice is rolled and the numbers that turn up are noted.

9 boys and 2 girls are to be placed next to each other in the school ground for morning assembly. What is the probability that there are exactly 4 boys between the 2 girls?

The probability of getting at most two heads when three coins are tossed simultaneously.

whenever horses a,b and c race together , their respective probabilities of winning are 0.3, 0.5 and 0.2. they race three times . (a) Find the probability that the same horse wins all three races . (b) Find the probability that a,b,…

Oranges chosen at random have a mean mass of 210 grams and a standard deviation of 35 grams. Assuming a normal distribution, what's the probability of choosing an orange with a mass between 170 grams and 250 grams?

Monthly food expenditures for families in Caloocan City average Php 4 500 with a standard deviation of Php 750. Assuming that the monthly food expenditures are normally distributed, what percentages of the expenditures are between Php…

The probability of getting at most two heads when three coins are tossed simultaneously.

Let T be a random variable giving the number of heads plus the number of tails in three tosses of a coin. List the elements of the sample space for the three tosses of the coin and assign a value to each sample point.

What is the probability that the height of a student picked at random has a height greater than 116 cm

Make a study about how many sheets of paper you consumed weekly in answering your self learning modules record the quantity total number of sheets per subject then construct a probability distribution compute the mean variance and the…

X=82

Two balls are drawn in succession without replacement from an urn containing 4 red balls and 5 blue balls. Let R be the random variable representing the number of red balls. Find the values of the random variable R.

Random samples with size 4 are drawn from the population containing the values 14, 19, 26, 31, 48, and 53 a. Construct a sampling distribution of the sample means. b. Find the mean of the sample means. c. Compute the …

julia and tony play and game rock paper scissor assume that at each play they make their choices with equal probability 1/3 for each of the three moves and dependently of any previous play A.)on any single play,what is …

Find the probability distribution of a random variable X representing the outcome when a single die is rolled once. 2 Three cards are drawn in succession from a deck without replacement. Find the probability distribution for th…

Four coins are tossed. Let Z be the random variable representing the number of tails.

Supposed to laptops or tested . If we let x be the random variable representing the number of defective laptops . What are the possible values of the random variable ?

A basket contains 10 red balls and 4 white balls.If three balls are taken from the basket one after the other,determine the possible values of the random variable R representing the number of red balls.

In a box are 2-balls one white and one yellow. Two balls are picked one at a time with replacement. Let X be the random variable representing the number of white balls.

Three balls are drawn in succession without replacement from an urn containing 3 red balls, 2 blue balls and 2 yellow balls. Let Z be the random variable representing the number of blue balls. Sample space (all outcomes) P…

In a betting game wherein the result may be one of the following in one turn: break even, win 5 peso or lose 3 peso. How much will be the amount a player gets after three turns. Let X be the total amount of a player gets after three t…

A shipment of five computers contains two that are slightly defective. if a retailer receives three of these computers at random, list the elements of the sample paces using the letters D and N for defective and non-defective computer…

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