Solved: Two balanced dice are rolled. Let X be the sum of two dice. Obtain the probability distribution of X

The scores for a mathematics course seem to be normally distributed with mean 70 & standard deviation of 8. If the instructor wishes to give an A grade to 10% of the students, what should be the dividing line between an A grade and a …

suppose the weight of 800 students are normally distributed with mean 75kg and standard deviation 5kg. find the numer of students that weigh more than 80kg

Suppose that the bank customers arrive randomly and independently on an average of 3.2 customers every 4 minutes. What is the probability that: a. Exactly two customers arrive in every 4 minutes? b. Exactly two customers will arriv…

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

To compare the results of boys and girls in a class, a special test was given to 50 boys who averaged 67.4 with Sd. of 5.0, and 50 girls averaged 62.8 with Sd. of 4.6. (Group Assignment) (2 pts.) a) Test, at …

To compare the results of boys and girls in a class, a special test was given to 50 boys who averaged 67.4 with Sd. of 5.0, and 50 girls averaged 62.8 with Sd. of 4.6. (Group Assignment) (2 pts.) a) Test, at   0.05 …

A manufacturer of paper used for packaging requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour's production…

Let X be a binomial(5, 0.2) random variable. Let Y be a discrete random variable that is independent of X, such that Y = 1 with probability 0.2 and Y = 0 with probability 0.8. What is the probability that the sum of X and Y is less th…

A dataset has a mean of 15 km and a standard deviation of 2 km with n equal to 30. There is a mode of 22 km and a median of 18 km with a range of 20 km. What is the variance?

According to a hospital administrator, historical records over the past 10 years have shown that 20 percent of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospita…

Four coins are tossed let z e the random variable representing the number of heads that turn up. find the values of the random variable Z

Supposed five coins are tossed.let x be the random variable representing the number of head occur. Find the probability of each values of the random variable.

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…

Using the sample in a family of four children, construct a probability distribution for the variable Z representing the number of boys. Draw the histogram of the probability distribution.

Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 oranges, with replacement being made after each drawing. Find the probability that (I) Both are white

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 the red balls

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

A student has to take 7 more courses before she can graduate. If none of the courses are prerequisites to others, how many groups of three courses can she select for the next semester?

An expirement study was conducted by a researcher to determine if a new time slot has an effect on the performance of pupils in Mathematics. Forty randomly selected learners participated in the study. Toward the end of the i…

A manufacturer of bicycle tires has developed a new design which he claims has an average lifespan of 15 years with standard deviation of 2 years. A dealer of the product claims that the average lifespan of 150 samples of th…

In a family with two children, find the mean of the number of children who will be girls

The lifetime of a light bulb is normally distributed with mean 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?

Suppose the IQ of the learners in a certain University follows a normal distribution with mean 110 and standard deviation 100? a What proportion of the learners population have IQ's more than 90 but less than 100? b. A random male …

The ages of participants in a drama workshop are normally distributed with mean 18.5 years and standard deviation 2.5 years. What is the probability that the age of a random participant is (a) more than 20 years, (b) between 16 and 18…

On the average, six people per hour use a self services banking facility during the prime shopping hours in a department store. Assuming the arrival of customers is random and independent; What is the probability that fewer than 5 peo…

In 2018, the braking distance of Toyota Camry cars on a wet surface follows a normal distribution. Its mean is 122 feet with a standard deviation of 20 feet. What is the probability that a randomly selected Toyota Camry will have a br…

On the average, six people per hour use a self services banking fasility during the prime shopping hours in a department store. Assuming the arrival of customers is random and independent; What is the probability that; One person will…

Students pass a test if they score 50% or more. The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively. Assuming this data is normally distributed, what perc…

The standard score of Mary in Chinese Test is 1.2 and her standard score in English Test is 0.8. In what subject did she perform better?

Students pass a test if they score 50% or more. The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively. Assuming this data is normally distributed, what perc…

1. The average weekly loss of labour hours due to factory accidents is studied on ten labours before and after a new industrial safety awareness program. The 95% confidence interval for the difference in mean of the weekly loss of lab…

A bakeshop owner determines the number of boxes of pandesal that are delivered each day. Find the mean of the probability distribution shown.

Type of random varial of number of black cards from an ordinary deck of cards

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?

According to a study by the Pew Research Center, 15% of adults in the US do not use the Internet. Suppose 10 adults in US are selected randomly. a. Is the selection of the 10 adults a binomial experiment? b. What is the pr…

find class boundaries, midpoint, and width for the class 18.8 - 22.6

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 the values 2,3,4,5 given that p(2)= 2/7, P(3)= 3/7, P(4) = 1/7, and P(5)= 1/7.

For each of the following scenarios, give an example of a discrete and a continuous random variable. The first one is done as an example. Scenarios •Asking your classmates about their breakfast. •M…

Let X be a discrete random variable such that X = 0 with probability 0.5 and X = 1 with probability 0.5. Let Y be a discrete random variable such that Y = 0 when X = 1 and Y = 1 when X = 0. What is the mean and variance of X + Y?

A box contains 5 green and 2 blue dice.Four dice are chosen one after the other .Determine the values of the random variable G representing the number of green dice.

4. A soft-drink machine is regulated so that it discharges an average of 200 mls per cup. If the amount of drink is normally distributed with a standard deviation equal to 15 mls. Below what value do we get the smallest 30% of the cup…

a taxi cab company has 12 ambassadors and 8 fiats. If 5 of these taxi cabs are in workshop for repair, calculate the probability that i) 3 of them are ambassadors and 2 flats ii) all the 5 are of the same make

1 4 4 2 3 4 5 1 4 1 Work out the mode

A spinner for a child's game has the numbers 1 through 9 evenly spaced. If a child spins, find each probability: a. The number is divisible by 3.

Suppose that the four inspectors at a film factory are supposed to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in ev…

Regression of yi = ꞵ0 + ꞵ1 xi1 + ꞵ2 xi2 + ꞵ3 xi3 + ꞵ4 xi4 + ui yields the following results in tabular form. The tabulated t- statistics is 2.6 , 1.96 and 1.64 for one , five and ten percent significance levels respectively. State the…

A spinner for a child's game has the numbers 1 through 9 evenly spaced. If a child spins, find each probability: a. The number is divisible by 3. b. the number is greater than 7. c. The number is an even number.

a) Consider the following functional relation, f, defined as: f : R \rightarrow R, f(x) = x2 Determine whether or not f is a bijection. If it is, prove it. If it is not, show why it is not. b) Consider the set F = {y | y = a…

Consider the lot of fluorescent tubes in number 100.if 50 samples of 100 tubes are drawn from the lot with replacement find the expected number of sample will have mean life atleast 1600 hrs. Flourescent tubes are 1570 hrs with a s.d.…

A recent survey found that 54.7% of the population own their homes. In a random sample of 150 heads of households, 92 responded that they owned their homes. At 0.01 level of significance does that indicate a difference from the nation…

Researcher is using data for a sample of 10 observations to estimate the relation between consumption expenditure and income. Preliminary analysis of the sample data produces the following data. ∑xy = 700 , 1000 2 ∑x = , ∑X = 1…

A report stated that the average age of commercial jets in country X is 14 years. An executive of a large airline company selects a sample of 36 planes and finds that the average age of the plane is 11.8 years. The standard deviation …

The odds of Matthew doing his math homework is 13:7. What is the probability of Matthew doing his homework once in the next two days?

Using the data given below, calculate the 3 and 5 years moving averages. Year 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 Sales 2354 2380 2319 2469 …

let x be a random variable with probability density function given by f(x)=(2he^-1/4x ; 0

A politician believes that 25% of all macroeconomists in senior positions would strongly support a proposal he wishes to advance. Suppose that this belief is correct and that five senior macroeconomists are approached at random. What …

FIND THE VALUES FOR EACH OF THE FF. CASES: A. UPPER TAIL AREA OF 0.025 WITH DEGREE OF FREEDOM=28 B. LOWER TAIL AREA OF 0.01WITH DEGREE OF FREEDOM=15 C. WHERE 90% OF THE AREA FALLS BETWEEN THESE TWO t-VALUES WITH df=9

the number of defective production in a production process follows a poisson distribution with a mean of 2.6 per month, for a given month what is the probability there will be fewer than two defective production?

According to the article "Are Babies Normal?" by Traci Clemons and Marcello Pagano published in The American Statistician, Vol. 53, No. 4, pp. 298-302, the birth weights of babies are normally distributed with a mean of 3388…

The owner of a factory that sells a particular bottled fruit juice claims that the average capacity of their product is 250 ml. To test the claim, a consumer group gets a sample of 100 such bottles, calculates the capacity of each bot…

According to the article "A Critical Appraisal of 98.6 Degrees F, the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich" published in the Journal of the American Medical Associ…

A factory manufacturing light-emitting diode (LED) bulbs claims that their light bulb last for 50 000 hours on the average. To confirm its this claim is valid, a quality control manager got a sample of 50 LED bulbs and obtained a life…

A box contains 18 light bulbs. Of these, four are defective. Five bulbs are chosen at random. What is the probability that four are defectives?

what happens to the variance of the sampling distribution of the sample means when the sample size increases

Determine if the following are probability distributions (if no, state why) x= {3,6,9,12,15} p(x)= {4/9,2/9,1/9,1/9,1/9}

The following represent the scores of a group of students on two tests. calculate spearman rs and kendall's tau for these data. Test 1 - 36, 34, 33, 29, 29, 28, 28, 28, 24, 22, 19, 12 Test 2 - 18, 26, 24, 18, 15, 12, 14, 13, 12, 10,…

1. To the left of z= -1.66 2.to the left of z=1.47 3.to the right of z=2.52 4.to the right of z= -1.75 5.between z=1.5 and 2.76

The following represent the scores of a group of students on two tests. calculate spearman rs and kendall's tau for these data. Test 1 - 36, 34, 33, 29, 29, 28, 28, 28, 24, 22, 19, 12 and Test 2 - 18, 26, 24, 18, 15, 12, 14, 13, 12, 1…

Three judges rated eight essays with the following results. Calculate the coefficient of concordance with these data. JUDGE ESSAY 1 2 3 1 8 7 8 2 6 5 6 3 4 6 5 4 1 2 1 5 3 3 2 6 2 1 3 7 5 4 4 8 7 8 7

The following data represent the operating time in hours for 4 types of pocket calculators before a recharge is required. Use the Kruskal-Wallis test, at the 0.01 level of significance, test the hypothesis that the operating times for…

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

The mean annual cost of car insurance is Rs 9450 and standard deviation of Rs 250. What is the probability that the average insurance cost of a sample of 25 cars will be between Rs 9400 and Rs 9500?

box a and box b contains 1,2,3,4. write the probability mass function and draw the histogram of the sum when one number from each box is taken at a time, with replacement

it is reported that 72% of the working women use computers at work. Choose 5 women at random and find the probability that at least 1 doesn't use a computer at work

determine if the following are probability distribution (if no, state why) X=1,2,3,4 and 5 P(x)= 3/10, 1/10, 1/10, 2/10 and 3/10

Construct a probability distribution of the random variable X for the number of false answers in a 4-item true or false test.

Construct probability distribution for the random variable X on the number of defective units selected when five units are chosen at random from a batch of ten flash drives which contains four defective items.

The water bills for residents in Davao City have a mean of Php2085 and a standard deviation of Php129. Random samples of 86 water bills are drawn from this population, and the mean of each sample is determined. What is the mean of the…

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 655 hours and a standard deviation of 21 hours. Random samples of 43 bulbs are drawn from this popul…

Find the proportion area of the region between z= -2 and z= -3

Population 1 consists of the values 5, 7, and 9. Population 2 consists of values (1, 5). Consider all the possible samples of size 2 that can be drawn with replacement from population 1 and all the possible samples of size 3 that can …

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 786 hours and a standard deviation of 80 hours. Find the probability that a random samples of 17 bul…

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 616 hours and a standard deviation of 54 hours. Random samples of 31 bulbs are drawn from this popul…

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 796 hours and a standard deviation of 55 hours. Find the probability that a random samples of 40 bul…

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 806 hours and a standard deviation of 90 hours. Find the probability that a random samples of 15 bul…

Let x denote the number of biased die with the following probability mass function p(x) X: 1 2 3 4 5 6 P(x): 1/6 1/6 1/5 y 1/5 1/6 a) find the value of y

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 780 hours and a standard deviation of 89 hours. Find the probability that a random samples of 31 bul…

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 798 hours and a standard deviation of 80 hours. Find the probability that a random samples of 39 bul…

Let x denote the number of biased die with the following probability mass function p(x) X: 1 2 3 4 5 6 P(x): 1/6 1/6 1/5 y 1/5 1/6 a) find the value of y b) find the cdf of x

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 810 hours and a standard deviation of 92 hours. Find the probability that a random samples of 39 bul…

a) Marks out of 100 for 100 students were tabulated as shown below: Marks f 11 – 20 4 21 – 30 16 31 – 40 27 41 – 50 32 51 – 60 15 61 – 70 4 71 – 80 2 i) Calculate the mean mark. (4 ma…

a presidential candidate asks a polling to conduct a nationwide survey to determine the percentage of potential voters who would vote for him over his rival presidential candidate. out of 2 500 respondents in the sample, 945 said they…

X: the number of automobile accidents per year in Virginia.

An overseas shipment of 5 foreign automobiles contains 2 that have slight paint blemishes. If an agency receives 3 of these automobiles at random, list the elements of the sample space S, using the letters B and N for blemished and no…

Let W be a random variable giving the number of heads minus 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 w of …

In a National Achievement Test, suppose three test booklets are tested at random. Let D represent the defective test booklet and let N represent the non-defective test booklet. Let X be the random variable representing the number …

In a survey, 1087 randomly selected adults were asked "Do you have occasion to use alcoholic beverages such as liquor, wine, or beer, or are you a total abstainer?" 62% of the subjects said that they used alcoholic beverages…

Two balanced dice are rolled. Let X be the sum of two dice. Obtain the probability distribution of X

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