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

Critical Reading 510 Mathematics 500 Writing 490

Assume that the population standard deviation on each part of the test is σ = 90.

a) What is the probability a random sample of 100 test takers will provide a sample mean

test score within 10 points of the population mean of 510 on the Critical Reading part of

the test?

b) What is the probability a random sample of 81 test takers will provide a sample mean test

score within 15 points of the population mean of 500 on the Mathematics part of the test?

c) What is the probability a random sample of 121 test takers will provide a sample mean

test score within 12 points of the population mean of 490 on the writing part of the test?

2) The average price of a gallon of unleaded regular gasoline was reported to be $3.90 in southwest Florida. Use this price as the population mean, and assume the population standard deviation is $.20.

a) What is the probability that the mean price for a sample of 36 service stations is within

$.05 of the population mean?

b) What is the probability that the mean price for a sample of 64 service stations is within

$.05 of the population mean?

c) What is the probability that the mean price for a sample of 100 service stations is within

$.05 of the population mean?

Critical Reading 510 Mathematics 500 Writing 490

Assume that the population standard deviation on each part of the test is σ = 90.

a) What is the probability a random sample of 100 test takers will provide a sample mean

test score within 10 points of the population mean of 510 on the Critical Reading part of

the test?

b) What is the probability a random sample of 81 test takers will provide a sample mean test

score within 15 points of the population mean of 500 on the Mathematics part of the test?

c) What is the probability a random sample of 121 test takers will provide a sample mean

test score within 12 points of the population mean of 490 on the writing part of the test?

2) The average price of a gallon of unleaded regular gasoline was reported to be $3.90 in southwest Florida. Use this price as the population mean, and assume the population standard deviation is $.20.

a) What is the probability that the mean price for a sample of 36 service stations is within

$.05 of the population mean?

b) What is the probability that the mean price for a sample of 64 service stations is within

$.05 of the population mean?

c) What is the probability that the mean price for a sample of 100 service stations is within

$.05 of the population mean?

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