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The following question is from Elementary Statistics in Social Research: The Scholastic Assessment Test is standardized...

The following question is from Elementary Statistics in Social Research:

The Scholastic Assessment Test is standardized to have population mean u=500 and a population standard deviation 0=100. Suppose that a researcher gives the SAT

to a random sample of 50 males and 50 females, yielding sample means of 511 and 541 respectively. Based on these samples' sizes the researcher has already calculated the true standard deviation of the sampling distribution of the difference between mean to be 20. Based on the areas under the normal curve given in Table A, find the probability of obtaining a sample mean for females that is at least 30 points higher than the sample mean for males.

I do not even know where to begin. Step by step explanation would be most appreciated.

Math   Statistics-And-Probability   
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Answer #1

The probability of obtaining a sample mean for females that is at least 30 points higher than the sample mean for males is obtained by calculating the z score for the difference in means as shown below,

Given:

Now,

The probability is obtained from the standard normal distribution table for z = 0

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