EF 507PS-Chapter 7FALL 2008
1. In a recent survey of college professors, it was found that the average amount of money spent on entertainment each week was normally distributed with a mean of $95.25 and a standard deviation of $27.32. What is the probability that the average spending of a sample of 25 randomly-selected professors will exceed $102.50?
A)0.0918
B)0.1064
C)0.3936
D)0.4082
2.The time it takes to complete the assembly of an electronic component is normally distributed with a standard deviation of 4.5 minutes. If we select 20 components at random, what is the probability that the standard deviation for the time of assembly of these units is less than 3.0 minutes?
A)<0.05
B)<0.005
C)<0.025
D)<0.01
QUESTIONS 3 THROUGH 6 ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that 20% of all invoices are for amounts greater than $800. A random sample of 50 invoices is taken.
3.What is the mean and standard error of the sample proportion of invoices with amounts in excess of $800?
A)Mean = 10, Standard error = 0.4472
B)Mean = 0.20, Standard error = 0.0566
C)Mean = 0.20, Standard error = 0.0032
D)Mean = 10, Standard error = 0.0598
4.What is the probability that more than 227% of these invoices are for more than $800?
A)0.1368
B)0.2266
C)0.3632
D)0.2734
5.Suppose that 15% of all invoices are for amounts greater than $1000. A random sample of 60 invoices is taken. What is the probability that at least 25% of these invoices are for more than $800?
A)0.1894
B)0.8106
C)0.3106
D)0.8894
6. Suppose that 15% of all invoices are for amounts greater than $1,000. A random sample of 60 invoices is taken. What is the probability that between 17% and 23% of these invoices are for more than $800?
A)0.2981
B)0.2019
C)0.0962
D)0.4038
7.The number of students using the ATM on campus daily is normally distributed with a mean of 237.6 and a standard deviation of 26.3. For a random sample of 55 days, what is the probability that ATM usage averaged more than 230 students per day?
A)0.9756
B)0.9483
C)0.9838
D)0.9524
8.A sample of size n is selected at random from an infinite population. As n increases, which of the following statements is true?
A)The population standard deviation decreases
B)The standard error of the sample mean decreases
C)The population standard deviation increases.
D)The standard error of the sample mean increases
9.Why is the Central Limit Theorem important in statistics?
A)Because for a large sample size n, it says the population is approximately normal.
B)Because for a large sample size n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.
C)Because for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.
D)Because for any sample size n, it says the sampling distribution of the sample mean is approximately normal.
10.If all possible random samples of size n are taken from a population that is not normally distributed, and the mean of each sample is determined, what can you say about the sampling distribution of sample means?
A)It is positively skewed.
B)It is negatively skewed.
C)It is approximately normal provided that n is large enough.
D)None of the above.
QUESTIONS 11 THROUGH 14 ARE BASED ON THE FOLLOWING INFORMATION:
Suppose you flip a coin four times. For every head, you receive one point, and for every tail, you lose one point.
11.Develop the sampling distribution for the mean number of points you receive from flipping four coins.
12.What is the standard error for the sampling distribution?
13.What is the probability that the mean number of points you receive on four flips is 0.5?
14.What is the probability that the mean number of points you receive on four flips is 0?
QUESTIONS 15 AND 16 ARE BASED ON THE FOLLOWING INFORMATION:
You have recently joined a country club. Suppose that the number of times you expect to play golf in a month is represented by a normally distributed random variable with a mean of 10 and a standard deviation of 2.4.
15.Over the course of the next year, what is the probability that you average more than 11 games a month?
16.Over the course of the next year, the probability is 85% that you average less than how many games per month?
17.The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4. For a particular sample size, the probability is 0.2 that the sample mean exceeds 300. How big must the sample be?
QUESTIONS 18 THROUGH 21 ARE BASED ON THE FOLLOWING INFORMATION:
It has been found that 62.1% of all unsolicited third class mail delivered to households goes unread. Over the course of a month, a household receives 100 pieces of unsolicited mail.
18.What is the mean of the sample proportion of pieces of unread mail?
19.What is the variance of the proportion?
20.What is the standard error of the sample proportion?
21.What is the probability that the sample proportion is greater than 0.60?
QUESTIONS 22 AND 23 ARE BASED ON THE FOLLOWING INFORMATION:
The filling machine at a bottling plant is operating correctly when the variance of the fill amount is equal to 0.3 ounces. Assume that the fill amounts follow a normal distribution.
22.What is the probability that for a sample of 30 bottles, the sample variance is greater than 0.5?
23.The probability is 0.10 that for a sample of 30 bottles, the sample variance is less than what number?
QUESTIONS 24 AND 25 ARE BASED ON THE FOLLOWING INFORMATION:
The average checking account balance at a local bank is $1,742 with a standard deviation of $132. A random sample of 70 accounts is selected.
24.What is the probability that the average balance for these accounts is less than $1,700?
25.The probability is 0.23 that the average balance for these accounts is greater than what amount?
26.The time it takes to complete the assembly of an electronic component is normally distributed with a standard deviation of 4.5 minutes. If we randomly select 20 components, what is the probability that the standard deviation for the time of assembly of these units was 50% more than the population standard deviation?
27.It has been estimated that 53% of all college students change their major at least once during the course of their college career. Suppose you are told that the sample proportion for a random sample was 0.48. Furthermore, you are told that the probability of getting a sample proportion of this size or smaller is 14%. What must have the sample size been?
QUESTIONS 28 THROUGH 31 ARE BASED ON THE FOLLOWING INFORMATION:
Given a population with mean =120 and variance = 81, the central limit applies when the sample size n. A random sample of size n = 36 is obtained.
28.What are the mean and standard deviation of the sampling distribution for the sample means?
29.What is the probability that the sample mean is greater than 123?
30.What is the probability that the sample mean is between 118 and 121?
31.What is the probability that the sample mean is at most 121.5?
QUESTIONS 32 THROUGH 35 ARE BASED ON THE FOLLOWING INFORMATION:
A random sample of size n =25 is obtained from a normally distributed population with population mean =200 and variance =100.
32.What are the mean and standard deviation of the sampling distribution for the sample means?
33. What is the probability that the sample mean is greater than 203?
34.What is the value of the sample variance such that 5% of the sample variances would be less than this value?
35.What is the value of the sample variance such that 5% of the sample variances would be greater than this value?
QUESTIONS 36 THROUGH 38ARE BASED ON THE FOLLOWING INFORMATION:
A random sample of 10 stock market mutual funds was taken. Suppose that rates of returns on the population of stock market mutual funds follow a normal distribution.
36.The probability is 0.10 that sample variance is bigger than what percentage of the population variance?
37.Find any pair of numbers, a and b, to complete the following sentence: The probability 0.95 that the sample variance is between a% and b% of the population variance.
38. Suppose that a sample of 20 mutual funds had been taken. Without doing the calculations, indicate how this would change your answer to question 2.
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