The College Board reported the following mean scores for the three parts of the

Question

The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): Assume that the population standard deviation on each part of the test is 100. Suppose that before the above information is released, you would like to use a sample of 90 test takers to estimate the population mean scores for the Mathematics part of the test. Can the sampling distribution of x be normally distributed? Why? What is the standard deviation of the sampling distribution of x(sigma_x)? What is the probability your sample will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Answer this question using the probability distribution table and manually carrying out the calculation Write down the Excel formula that can give you the answer for part c. What is the resulting answer?

Explanation / Answer

a) Yes, as the sample size is large enough (>30) , as per central limit theorum, distribution of xbar wiil be normal

b) std deviation of sample mean =std deviation of population/(sample size)1/2 =100/(90)1/2=10.5409

c) as in normal distribution z=(X-mean)/std deviation

P(-10/10.5409<Z<10/10.5409) =P(-0.9487<Z<0.9487)=0.8286-0.1714=0.6572

d) you can use norm.dist for calculation by mean score or normsdist for calculation by z score.

please revert for further clarification

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