1. A set of final examination grades in a course is normally distributed with a population mean of 75 and a population standard deviation of 10. What is probability of getting a grade of 90 or more on...

1. A set of final examination grades in a course is normally distributed with a population mean of 75 and a population standard deviation of 10. What is probability of getting a grade of 90 or more on this exam? (4 points)

(A XXXXXXXXXX

(B XXXXXXXXXX

(C XXXXXXXXXX

(D XXXXXXXXXX

XXXXXXXXXX% of the students taking the test scores higher than what grade? (4 points)

(A) 79

(B) 83

(C) 89

(D) 92

1. If the professor grades on a curve (i.e., gives A’s to the top 10% of the class, regardless of the score), are you better off with a grade of 80 on this exam or a grade of 70 on a different exam, where the mean is 65 and the standard deviation is 5? (4 points)

1. I am better off on this exam, where the mean is 75 and the standard deviation is 10.
2. I am better off on the other exam, where the mean is 65 and the standard deviation is 5.

1. At a computer manufacturing company, the actual size of computer chips is distributed with a mean of 1 centimeter and a population standard deviation of 0.15 centimeter. A random sample of 25 computer chips is taken.

1. What is the probability that the sample mean will be greater than 1.01 centimeters? (Please show your calculation, 4 points)

1. To solve this problem, do you need to make any assumption about the population distribution? Why? (4 points)

1. Which of the following statement is not correct? (4 points)

(A) For most population distributions, regardless of shape, the sampling distribution of the mean is approximately normally distributed if samples of at least 30 are selected.

(B) If the population distribution is fairly symmetrical, the sampling distribution of the mean is approximately normal for samples as small as 5.

(C)If the population is normally distributed, the sampling distribution the mean is normally distributed regardless of the sample size.

(D) For most population distributions, regardless of shape, the sampling distribution of the mean is approximately normally distributed if samples of at least 20 are selected.

6. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.6 pounds, what is probability distribution of the sample mean? (4 points)

1. The sample mean will follow a normal distribution with a mean of 3.2 pound and standard deviation of 0.8 pound.

1. The sample mean will follow a normal distribution with a mean of 3.6 pound and standard deviation of 0.8 pound.

1. The sample mean will follow a normal distribution with a mean of 3.2 pound and standard deviation of 0.16 pound.

1. None of the above is right.

Use the information given below to answer questions 7-10:

The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. It is known from the manufacturer’s specifications that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 25 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.995 gallon.

1. What kind of critical value should you use? (4 points)
1. Z value
2. t value

1. Construct a 95% confidence interval estimate for the population mean amount of paint included in a 1-gallon can. (4 points)

A. between XXXXXXXXXXand 1.2469

B. between XXXXXXXXXXand 1.0028

C. between XXXXXXXXXXand 1.1546

D. between XXXXXXXXXXand 2.5879

1. Is there reason to believe that the population mean is different from 1 gallon? (4 points)

1. Yes.
2. No.

1. Do you need any assumption about the population distribution to construct the interval estimate? (4 points)

A. Yes.

B. No.

11. If , s =24, and n=36, construct a 95% confidence interval estimate of the population mean µ. (4 points)

A. between XXXXXXXXXXand XXXXXXXXXX

B. between XXXXXXXXXXand XXXXXXXXXX

C. between XXXXXXXXXXand XXXXXXXXXX

D. between XXXXXXXXXXand XXXXXXXXXX

Use the information given below to answer the question 12-20:

ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. But if too much cash is unnecessarily kept in the ATMs, the bank is forgoing the opportunity of investing the money and earning interest. Suppose that at a particular branch the population mean amount of money withdrawn from ATMs per customer transaction over the weekend is $160 with a population standard deviation of $20. If a random sample of 25 customer transactions indicates that the sample mean withdrawal amount is $164, is there evidence to believe that the population mean withdrawal amount is no longer $160? (Use a 0.05 level of significance)

12. State the null and alternative hypothesis. (4 points)

1. Ho: µ
2. Ho: µ ≥ 160; Ha: µ ≠ 160
3. Ho: µ ≥ 160; Ha: µ
4. Ho: µ = 160; Ha: µ ≠ 160

13. What test should be used to reject the null hypothesis? (4 points)

1. Z test two tail
2. t test two tail
3. Z test one tail
4. t test one tail

1. Assuming the significance level is 0.05, what is the critical value that you should use? (4 points)

A. 1.96

B. 1.64

C. -1.96

D. -1.64

1. What is the computed value of the sample statistic? (4 points)

A. - 1

B. -1.75

C. 1

D. 1.75

1. what are the decision and conclusion of the test at the significance level of 0.05? (4 points)

1. Fail to reject the null hypothesis, there is sufficient evidence to conclude that the mean amount of cash withdrawn per customer from the ATM machine is not equal to $160.
2. Fail to reject the null hypothesis; there is insufficient evidence to conclude that the mean amount of cash withdrawn per customer from the ATM machine is not equal to $160.
3. Reject the null hypothesis; there is sufficient evidence to conclude that the mean amount of cash withdrawn per customer from the ATM machine is not equal to $160.
4. Reject the null hypothesis; there is insufficient evidence to conclude that the mean amount of cash withdrawn per customer from the ATM machine is not equal to $160.

1. what is the p-value? (4 points)

1. 0.10
2. 0.16
3. 0.20
4. 0.32

1. what is the meaning of the p-value? (4 points)

A. The probability of observing a Z test statistic more extreme than the computed sample test statistic is 0.10 if the population mean is indeed $160.

B. The probability of observing a Z test statistic more extreme than the computed sample test statistic is 0.16 if the population mean is indeed $160.

C. The probability of observing a Z test statistic more extreme than the computed sample test statistic is 0.20 if the population mean is indeed $160.

D. The probability of observing a Z test statistic more extreme than the computed sample test statistic is 0.32 if the population mean is indeed $160.

1. What is the conclusion if you use the p-value approach? (4 points)

1. Reject the null
2. Accept the null

1. Do you need any assumption about the population distribution to conduct the test? (4 points)

1. Yes
2. No

21 . In New York State, savings banks are permitted to sell a form of life insurance called Savings Bank Life Insurance (SBLI). The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service. During a period of one month, a random sample of 25 approved policies is selected and the sample average processing time is 40 days and sample standard deviation is 25 days. In the past, the mean processing time average 45 days. At the 0.05 level of significance, is there evidence that the mean processing time has become shorter than 45 days? (Please use both critical value approach and p-value approach to conduct the hypothesis testing, 16 points, without calculation process you will get zero point.)