Q1)

The College Board reported the following mean scores for three parts of the Scholastic Aptitude Test (SAT):

Critical Reading 502;

Mathematics 515;

Writing 494

Assume that the population standard deviation on each part of the test is 100. 1.1. For a random sample of 64 test takers, find the standard deviation of the sampling distribution of the sample mean.

1.2. What is the probability that a random sample of 64 test takers will provide a sample mean test score of within 10 points of the population mean of 502 on the Critical Reading part of the test?

1.3. For a random sample of 100 test takers, find the standard deviation of the sampling distribution of the sample mean.

1.4. What is the probability that a random sample of 100 test takers will provide a sample mean test score of within 10 points of the population mean of 515 on the Mathematics part of the test?

Q2)

The average price per gallon of unleaded regular gasoline was reported to be $2.34 in northern Kentucky. Use this price as the population mean, and assume that the population standard deviation is $0.20.

2.1. For a random sample of 64 service stations, find the standard deviation of the sampling distribution of the sample mean.

2.2. What is the probability that the mean price for a sample of 64 service stations is within $0.03 of the population mean?

2.3. For a random sample of 100 service stations, find the standard deviation of the sampling distribution of the sample mean.