Solved: A box contains 5 balls. One is numbered 1, three are numbered 2, and one is numbered 3. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the mean of the numbers on the balls

A random sample of size 16 has 53 as mean. The sum of the squares of the deviation taken from mean is 150. Can this sample be regarded as taken from the population having 56 as mean? Obtained 95% and 99% level of confidence limi…

The following data shows heights in centimeters of 10 persons selected at random from a village. Find out whether, it would be reasonable or justifiable to suppose the height of that village population as 182 cm. The heights …

The number of taxis waiting at a cab stand is thought to follow a uniform distribution. The number present was recorded at 50 random times:Use the appropriate goodness of fit test to determine if the uniform distribution is a good ch…

Construct a probability distribution table if we let X the random variable be the number of boys in the family with 3 children.

The variance of the number of cars sold per day is 2.27 what is the Standard deviation of the cars per day?

From the past experience of software quality testing, it is known that the probability of the presence of an error in coding is 0.05. If the probability of a tester detecting an error when the error is present is 0.78 and the probabil…

A basket contains 10 ripe and 4 unripe bananas. If three bananas are taken from the basket one after the other, determine the possible values of the random variable U representing the number of unripe bananas

The mean monthly sale of a particular household item in department stores was observed as 133.3 units per store. After an advertising campaign, data on sales of this item from 25 stores were collected and it is found that the mean sal…

The number of taxis waiting at a cab stand is thought to follow a uniform distribution. The number present was recorded at 50 random times: Number of taxis 0 1 2 3 4 5 6 7 8 Frequency 4 6 8 5 7 6 6 5 3 Use the appropriate goodness of …

a factory is manufactures face masks that widely used during pandemic covid-19. it is found that on average, 10% of the face masks produced are defective. if 150 face masks are randomly selected, what is the probability that the numbe…

True or False. (i) Age of a student is a discrete data. (ii) Mean is not affected by extreme values. (iii) A histogram can not be made for categorical data. (iv) ∑ 5 20 7 = 70. (v) The spread of a single value is always zero. (v…

An operation is carried out by a subsystem consisting of three units that operate in a series configuration. (a) The units have exponentially distributed lifetimes with mean 1. How many subsystems should be operated in parallel to a…

if random variable is uniformly distributed (-2,1) find pdf of y = 2x ^3

Consider a population consisting of 5 units with the following values of a variable Y: 29, 87, 94, 10, 13. A simple random sample of size 3 is picked from this population without replacement. i. Write down all the possible simple rand…

2) Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The following table shows the shipping costs per truck…

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 f…

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…

Determine the area under the standard normal distribution curve between z=1.15 and z=-1.85

1) How do drivers react to sudden large increases in the price of gasoline? To help answer the question, a statistician recorded the speed of cars as they passed a large service station. He recorded the speeds (mph) in the same lo…

The number of cars sold per day at a local car dealership, along with its corresponding probabilities, is shown in the table. Compute for the mean, variance, and standard deviation of the probability distribution of the random variabl…

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…

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…

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…

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?

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

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…

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…

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?

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…

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…

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 …

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…

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

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

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 …

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

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,?

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 …

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…

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…

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…

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…

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…

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…

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}

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 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?

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

"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 …

"An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 984 hours and a standard deviation of 52 hours. Random samples of 41 bulbs are drawn from this…

"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…

"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 …

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…

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…

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…

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 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 balls are drawn in succession without replacement of an containing 5 white balls and 6 black balls Let B be the random variable representing the number of black balls. Construct the probability distribution of the random variable R

The recommended retail price of a brand of designer jeans is known. The price of the jeans in a sample of 16 retailers is on average $141 with a sample standard deviation of 4. If this is a ‘random’ sample and the prices can be assume…

In a wage discrimination case involving male and female employees, it is assumed that male employees have a mean salary equal to that of female employees. To justify this, independent random samples of male and female employees were t…

Two groups of children were given visual acity tests,group.group 1 was composed of 11 children who receive their health care from private physician.the mean score for this group was 26 with standard deviation of 5.group 2 was composed…

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

1. For each of the following, determine whether it can serve as the probability distribution of some random variable: a) p(k) = 1/7 , for k = 0; 1; 2; 3; 4; 5; b) p(x) = x2 /30 , for x = 0; 1; 2; 3; 4; c) p(y) = (y+4)/(y-4) , for y…

7. A frozen food distributor claims that 80% of its frozen chicken dinners contain at least three ounces of chicken. To check the claim, a consumer testing service decides to check ten of these chicken dinners and rejects the claim un…

8. A quality control engineer wants to check whether, in accordance with speci cation, 90% of products shipped are in perfect working condition. To this end, she randomly selects 12 items from each lot ready to be shipped and passes t…

11. Find z if the standard normal-curve area a) between 0 and z is 0.4726; b) to the left of z is 0.9868; c) to the left of z is 0.3085; d) between -z and z is 0.9282 12. If a random variable has the normal distribution with &b…

15. The grapefruits grown in a large orchard have a mean weight of 18.2 ounces with a standard deviation of 1.2 ounces. weights of these grapefruits has roughly the shape of a normal distribution, what percentage of the grapefruit wei…

18. The lengths of fully-grown scorpions of a certain variety have a mean of 1.96 inches and standard deviation of 0.08 inch. Assuming that the distribution of these lengths has roughly the shape of a normal distribution, find what pe…

22. For a chi-square distribution,find x2\alpha such that a) P(X2 > x2\alpha) = 0:99 when df = 4; b) P(X2 > x2\alpha) = 0:025 when df = 19; c) P(37.652 < X2 < x2\alpha) = 0:045 when df = 25. 23. Find a) t0.…

1. An urn contains 4 balls numbered 1, 2, 3, 4, respectively. Let Y be the number that occurs if one ball is drawn at random from the urn. What is the probability function for Y ? 2. Consider the urn in Exercise 1. Two balls are …

5. A class in statistics contains 10 students, 3 of whom are 19, 4 are 20, 1 is 21, 1 is 24, and 1 is 26. Let X be the average age of the 2 randomly selected students and derive the probability function for X. 6. A man has four k…

1. A population random variable is normally distributed with a mean of 50 and a variance of 16. If a random sample of size n = 25 is drawn from this population, what are the following probabilities? a) that the sample mean will exc…

5. Random samples of size n were selected from binomial populations with population parameters p given here. Find the mean and the standard deviation of the sampling distribution of the sample proportion ^p = X \bar in each case…

7. 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 product…

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…

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 box contains 5 balls. One is numbered 1, three are numbered 2, and one is numbered 3. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the mean of the numbers on the balls

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Question ID: mtid-4-stid-46-sqid-2584-qpid-1054