Solved: Lawrence performs a survey to determine the average number of minutes of exercise seventh-grade athletes get in one week. He gets a list of sports and the seventh-grade students participating in each sport. He then chooses 10 people from each list to complete the survey. How can Lawrence’s sample be improved to be more representative of the population?

The number X of days in the summer months that a construction crew are cannot work because of the weather has the probability distribution X P(x) 6 0.03 7 0.08 8 0.15 9 0.20 10 0.19 11 0.16 12. 0.10 13 0.0…

7. An arithmetic test is given twice within a few days to a student. The highest possible score is 40. He receives a score of 35 the first time and a score of 18 the second time. If similarly varying results are obtained with other st…

In 2012 the Centers for Disease Control and Prevention reported that the rate of autism in children has risen to in 50. A study conducted in Norway suggests that the risk of autism may be significantly lower if women take folic acid s…

Suppose three test kits are tested at random. Let N be the random variable for the number of non - defective test kits, construct the probability distribution P(N). What can you conclude about the effectivity of the COVID-19 Rapid Ant…

Mrs. Paul wants to test that claim that, on average, her students' average mark is 85. She pulls the records of 100 per past student over a three-year period. The grades are inputted into MINITAB for analysis. Exhibit 1 below shows th…

a car salesperson as arrange a visit on three perspective customers in a week based on the past experiences helpers and laws that there is 10% chance of closing a sale on each visit determine the probability distribution of the number…

find the mean of the probability distribution of the random variable X and interpret its value, which can take only the values of 3,5, and 7, given that P (3) = ⁷/³⁰, P(5) = ⅓ and P(7) = ¹³/³⁰

Let the sample space be S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely. Compute the probability of the event E="an even number less than 7."

The probability that a tutor will see 0, 1, 2, 3, or 4 students x 0 1 2 3 4 P(x) 4/27 1/27 5/9 ? 5/27 (a) What is the probability that the tutor sees 3 students? (b) What i…

The number X of days in the summer months that a construction crew are cannot work because of the weather has the probability distribution X P(x) 6 0.03 7 0.08 8 0.15 9 0.20 10 0.19 11 0.16 12…

Jac tossed an unbiased coin. If the coin lands with head up on each toss, he wins ₱50. However, if it lands with tail up, he loses ₱60. If he continues to play the game, how much can he expect to win or lose in the game?

You are in a carnival and you see a game. The rule says that the outcome in the game is a random variable from 1 to 14 and that if the outcome is even, you win ₱50. If the outcome is odd, you win nothing. If you play the game, what …

Question 2 The probability that a house in an urban area will be burglarized is 5%. A sample of 50 houses is randomly selected to determine the number of houses that were burglarized. P (pass) = 0.05 q (failure) = 0.95 n = 50 (a) …

A coin is tossed four times. b. Suppose the outcome of the first two tosses are heads, and Y represents the number of heads landed, what are the possible values of Y?

The equations of two Regressions lines are 7𝑥 − 16𝑦 + 9 = 0 and 5𝑦 − 4𝑥 − 3 = 0. Find the coefficient of correlation and the means of x and y

Supposed three coins are tossed. Let X be the random variable representing the number of heads occur . Construct a table that shows the sample space and values of the random variable X

Question 3 A sales firm receives an average of three calls per hour on its toll-free number. Suppose you were asked to find the probability that it will receive at least three calls, in a given hour: (a) (i) which distribution does…

Zelazo et al. (1972) investigated the variability in age at first walking in infants. Study infants were grouped into four groups, according to reinforcement of walking and placement: (1) active (2) passive (3) no exercise; and …

find the range, standard deviation and range of 8 10 22 18 17 11 15 28 16 16

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

Find the mean of the probability distribution of the random variable X which can take only values 2,4,5, and 9, given that P(2)=9/20, P(4)=1/20, P(5)=⅕, P(9)=3/10

Three balls are drawn in succesion without replacement from a box of 2 red balls. Let R be the random variable representing the number of red balls. Find the values of the random variable R. Complete the table below

1. i. Compare Z distribution and Normal Distributions. ii. What are the properties of the t distribution? iii. Find the values for each. a. t 𝛼/2 and n = 15 for the 98% confidence interval for the mean b. t 𝛼/2 and n = 10 fo…

1. i. What happens to the margin of error when sample size increases? Does it increase, decrease, or stay the same? ii. How does this affect the size of the resulting confidence interval?

Ramdon sample of size 4 are drawn froem the finite population which consists of the number 2,3,7,8 and 10

1. Suppose we are interested in finding a 99% confidence interval for the mean overall score of students at a certain school. Five students are sampled, and their overall scores are 560, 500, 470, 660, and 640. a. What is th…

1. Suppose our p-value is .044. What will our conclusion be at alpha levels of .10, .05, and .01?

1. At a certain college, new students are weighed when they join the college, new students are weighed when they join the college. The distribution of weights of students at the college when they enroll has a standard deviation of 7.5…

Suppose Billy scored a 54 on his exam. The mean of the grade is 66 and the standard deviation is 3.what is the z score?

1. For a sample of 35 items from a population for which the standard deviation is σ= 20.5 , the sample mean is 458.0. At the 0.05 level of significance, test H0: μ= 450 versus H1: μ> 450 . Determine and interpret the p-value for the…

How many possible random samples of size 4 can be drawn from a population of size 8?

Four coins are tossed. Let A be the random variable representing the number of heads that occur. Find the values of the random variable A. Possible Outcomes Value of the Random Variable A (Number of Heads)

Six women and five men walk into an appliance store at the same time. There are five salesperson available to help them.Find the probability that a salesperson will first help at least 2 women.

The average weight of 25 chocolates bars selected from a normally distributed population is 200 g with a standard deviation of 10 g. Fight the point and the interval estimates using 95% confidence level.

Find the finite population correction factor given the following: 1. N=200, n=20 2. N=250, n=10 3. N=2000, n=15 4. N=2500, n=20 5. N=200, n=20

The level of significant and critical region a=,df=,and the t critical=

Four coins are tossed. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z. * Captionless Image The possible values of the random variable Z are 1, 2, and 3. …

he Surf-excel company uses a machine to fill boxes with soap powder. Assume that the net weight of the boxes of soap is normally distributed with mean 15 ounces and standard deviation 0.8 ounces. 25% of the boxes will be heavier than …

Two cards are drawn from a deck. How many possible values can each of the following variables take? 1. sum of the numbers on the cards ___________ 2. number of times both cards are black ________ 3. Number of …

2. Gillbert got a new job in a shoe store. The number of pairs of shoes he was able to sell for three days are 2, 4, and 5. Assume that samples of size 2 are randomly selected with replacement from this population of three values. a.…

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 S for the three tosses of the coin and to each sample point assign a value.

Given the data 6, 9, 12, 15, 16, 19, 22. Construct a sampling distribution of the sample mean without replacement and repetition by selecting 2 samples at a time.

1. The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 260 minutes and a standard deviation of 50 minutes. a. What is the probability that a battery lasts more…

1. Based from record, the mean weight of the newborn babies is 4.8 lbs with a standard deviation of 0.75 lbs. Out of 60 new born babies, find: a. The probability that the sample mean is less than 4.6 lbs b.The probability th…

1. Let X be random variable with values 4,5,6,7,8 and 9 a. Find the mean and the variance of the sample without replacement of n=2. b. Find a the sampling distribution of the mean and construct it's histogram 2. A…

A certain population has a mean of 15.4 and a standard deviation of 5.6. if random samples of size 5 is taken from this population, which of the following statements is true? * 1 point The standard deviation of the sampling distri…

A meeting of envoy was attended by 5 Koreans and 3 Filipinos. If four envoy were selected at random one after the other determine the values of the random variable K representing the number of Koreas.

1. Each main bearing cap in an engine contains 4 bolts. The bolts are selected at random without replacement from a parts bin that contains 30 bolts from one supplier and 70 bolts from another. a. b. What is the probability …

Observe yourself in a day. Find out how many hours you spend in the following activities: house chores, answering Self Learning Modules, planting/gardening, using social media like Facebook, messenger, tiktok, Instagram, and YouTube, …

Suppose the mean height of 200 students was 150 cm with a standard deviation of 12cm and mean weight was 60 kg with a standard deviation of 7kg

A firm employs 300 women and 100 men. The mean number of days absent last year for the women was 5.3 with a s.d. of 2.2 and for the men the corresponding figures were 6.2 and 2.9. Is the difference between the means significant at 5% …

How many possible samples of size n=8 can be drawn from a population of size 11

Permutation and Combination: In how many ways can 7 students be selected in a row of 7 seats if 2 of the students insist of sitting beside each other? In a gathering, the host make sure that each guest shakes hands with everyone else…

1. A coin is tossed twice. If the second throw results in tail a die is thrown. Describe the sample space for this experiment.

2. A random experiment has m outcomes a1,a2....,am and another has out out comes b1,b2.......,bn. Describe the sample space when both the experiment carried out.

3. A box contains 4 bad and 6 good tubes. Two are drawn out from the box at a time. One is tested and found to be good. What is the probability that the other one is also good?

How large a sample should be taken to be 95% sure that the error of estimation does not exceed 0.2 unit when standard deviation is 5?

How many people are likely to have a birthday that reads palindromically within their lifetime? (i.e.22/02/2022)

A laboratory supervisor in hospital is investigating number of reported on-the-job training accidents over a period of one month. Based on past records, she has derived the following probability distribution for x; where x is the numb…

From a box containing 4 black balls and 2 green balls, 3 balls are drawn in succession. Each ball is placed back in the box before the next draw was made. Let G be a random variable representing the number of green balls that occur. F…

Discrete or Continuoes sThe number of glasses in a dishwasher * 2 point Discret Continuouses The number of dropouts in a school per district The time taken to complete a puzzle The volume of water in a bottle

A Average Senior high school annual cost of tuition fee for all private schools last year was php 43.700. a random sample of cost this year for 45 private schools indicated that the sample mean was 45,800 and a sample standard deviati…

Two coin's are tossed. Let H be the number of Tails that occur. Determine the values of the random variable H.

In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at random will lie a. above score 50? b. below score 38? c. between 35 a…

Let Y be the random variable representing the number of tails that occur. Find the values of the random variable Y

A committee of 6 can be formed from a group of 5 sophomores, 7 juniors, and 8 senior. In how many ways can these be done if: A. there are 2 members from each class on the committees B. there shall be exactly 3 seniors, 2 jun…

70 years, and the standard deviation was 5.1 years. If a sample of 50 people from this region is selected, what is the probability that the mean life expectancy will be less than 71 years?

Number of times the first card is face card and the second card is not face card

A population consists of the five measurements 1, 3, 4, 6, and 8. Suppose samples of size 3 are drawn from this population. Construct a table, solve for the mean, variance and standard deviation.

When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 39 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3…

Suppose three coins are tossed. Let S be the random variable representing the number of heads that occur. Determine the sample space and the values of a random variable

As a fundraiser, the drama club decides to sell candy and cookies at noon hour. The club can purchase supplies from the cafeteria and may choose to buy from the following list if items:  five types of chocolate bars  four types …

In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at random will lie c. between 35 and 53?

Find the are to right of z=2.78

The numbers 5, 10, 15, and 20 are written on slips of paper, which are then placed in a hat. Two slips are randomly selected with replacement. Find the mean of the samples where the first is smaller than the second.

A basket contains 8 ripe and 6 unripe bananas. If three bananas are taken from the basket one after the other. Construct a table that shows all the possible outcomes of the random experiment and all the values of the random variable R…

(b) Patients arrive at a hospital accident and emergency department at random at a rate of 6 per hour. Find the probability that, during any 90 min. period, the number of patients arriving at the hospital accident and emergency …

When preparing a bouquet, a florist can choose from seven roses, six carnations, and four chrysanthemums. How many bouquets can the florist make if the bouquet must have at least one flower?

A stockroom clerk returns three safety helmets at random to three steel mill employees who had previous checked them. If Gary, Yuri and Cris, in that order, receive one of the three hats, list all the sample points for the possible or…

The probability density shown in Figure 5.21 is the exponential distribution f (x) = 0.55 e−0.55x 0 < x 0 elsewhere Find the probability that (a) the time to observe a particle is more than 200 microseconds; (b) the time to…

A change is made to one product page on the retail companies’ web site. To determine if the change does improve the efficiency of that product page, data must be collected on the proportion of visitors to the new page that ultimat…

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 me…

A fair spinner has 9 equal sections: 2 red, 3 blue and 4 green. It is spun twice. What is the probability of getting not green then green?

Suppose three cellphones are tested at random.let D represent the defective cell phone and N represent the non defective cellphone.if we let X be the random variable for the number of defective cellphones,construct the probability dis…

Two coins are tossed. Let H be the number of tails that occur.Determine the values of the random variable H.

A meeting of envoys was attended by 4 Koreans and 4 Filipinos. If three envoys were selected at random one after the other, determine the values of the random variable K representing the number of Koreans.

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. with the distribution of 0.75

If the probability density function of a random variable X is given by 𝑓(𝑥) = {2𝑘𝑥𝑒 − 𝑥2 , 𝑥 > 0 0, 𝑥 ≤ Determine (i)k (ii)distribution function.

If the two coins are tossed which is not a possible value of the random variable for the number of tails

The probabilities of machine manufacturing 0,1,2,3,4 and 5 defective parts in one day are 0.75,0.17,0.04,0.025,0.01 and 0.05 respectively. Find the mean of the probability Distribution

Four coin are tossed, let Z be the random variable representing the number of heads that turn up.find the value s of the random variable Z.

Four coins are tossed, Let H represent the head and T represent the tail. Let Y be the random variable representing the number of tails that occur. List all the possible outcomes and the corresponding values of the random variable Y

The ages of SHS students enrolled at ISNHS are normally distributed with a mean of 17 years and a standard deviation of 2.5 years. If a student is selected at random, what is the probability that his age is under 16 years?

A man has three routes from his home and he is equally likely in choosing these three ways.the chance that he will miss the train on choosing these three ways are respectively .25,.3,.35.one day he missed train find the probability th…

Find each of the following percentile points under the normal curve. Complete your procedures and find the corresponding z-score of each problem. Paragraph 2. Between z=-0.78 and z=-1.95 2. P32 1. P99

A reasearcher chose the participants of his study by selecting every 8th member of the population

The heights of Grade 11 male students in your school are normally distributed with a mean of 168 cm and standard deviation of 10 cm. Describe sampling distribution of 25 students wo are randomly drawn from the population.

The probabilities that a surgeon operates on 3, 4, 5, 6, or 7 patients in any one day are 0.15, 0.20, 0.25, 0.20 and 0.20, respectivel

Plasma glucose levels are used to determine the presence of diabetes. Suppose the mean ln (plasma-glucose) concentration (mg/dL) in 35- to 44-year-old is 4.86 with a standard of 0.33. A sample of 26 sedentary people in this age group …

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