Question

The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009):

Critical Reading 502

Mathematics 515

Writing 494

Assume that the population standard deviation on each part of the test is = 100. Use z-table.

What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places.

What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places.

What is the probability a sample of 100 test takers will provide a sample mean test score within 10 points of the population mean of 494 on the writing part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places.

Answer 1

1)

Using Central Limit theorem, we know,

Required probability =

2)

Using Central Limit theorem, we know,

Required probability =

3)

Using Central Limit theorem, we know,

Required probability =