Exam 7: Sampling and Sampling Distributions

MNM Corporation gives each of its employees an aptitude test. The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. A simple random sample of 25 is taken from a population of 500. a.What are the expected value, the standard deviation, and the shape of the sampling distribution of ? b.What is the probability that the average aptitude test in the sample will be between 70.14 and 82.14? c.What is the probability that the average aptitude test in the sample will be greater than 82.68? d.What is the probability that the average aptitude test in the sample will be less than 78.69? e.Find a value, C, such that P(11ecf06b_be84_96e5_b512_aff0a4e65f1e_TB2075_11 ≥ C) = .015.

In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study. a.What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178? b.What is the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025?

A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have

Ten percent of the items produced by a machine are defective. A random sample of 100 items is selected and checked for defects. a.Determine the standard error of the proportion. b.What is the probability that the sample will contain more than 2.5% defective units? c.What is the probability that the sample will contain more than 13% defective units?

Exhibit 7-3 In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. -Refer to Exhibit 7-3. The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is

A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is

In a restaurant, the proportion of people who order coffee with their dinner is .9. A simple random sample of 144 patrons of the restaurant is taken. a.What are the expected value, standard deviation, and shape of the sampling distribution of? b.What is the probability that the proportion of people who will order coffee with their meal is between 0.85 and 0.875? c.What is the probability that the proportion of people who will order coffee with their meal is at least 0.945?

Exhibit 7-1 A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. -Refer to Exhibit 7-1. In this problem the 0.22 is

A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $300 with a standard deviation of $48. A random sample of 144 checking accounts is selected. a.What is the probability that the sample mean will be more than $306.60? b.What is the probability that the sample mean will be less than $308? c.What is the probability that the sample mean will be between $302 and $308? d.What is the probability that the sample mean will be at least $296?

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were female. The standard error of the proportion is

The standard deviation of a point estimator is called the

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the

There are 6 children in a family. The number of children defines a population. The number of simple random samples of size 2 (without replacement) which are possible equals

Since the sample size is always smaller than the size of the population, the sample mean

A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the sample mean will be between 183 and 186 is

A simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained. A point estimate of the mean is

A sample of 400 observations will be taken from an infinite population. The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is

The expected value of the random variable is

An experimental diet to induce weight loss was followed for one week by a randomly selected group of 12 students with the following results. a.Find a point estimate for the average amount lost after one week on this diet. Is this an unbiased estimate of the population mean? Explain. b.Find a point estimate for the variance of the amount lost on this diet. Is this an unbiased estimate of the population variance? Explain. c.Find a point estimate for the standard deviation of the amount lost on this diet.