# STATISTICS 141-In the population ACT scores are normally distributed

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## STATISTICS 141-In the population ACT scores are normally distributed

4. In the population ACT scores are normally distributed with a mean of 18 and a standard deviation of 6. Suppose that we are taking a simple random sample of 40 students from one high school. [30 points]A. Calculate the standard error of the mean.B. If we were to repeatedly pull samples of 40 individuals from the population of all ACT test takers, the distribution of sample means would have a mean of ____ and a standard deviation of ____.C. Given the values from part B, 95% of random samples of will have sample means between ___ and ___.D. What is the probability that you would pull a random sample of 40 individuals from the population of all test takers and they would have a sample mean of 19 or higher?E. Suppose that the high school in question boasts that their students (i.e., the population of all of their students) have an average ACT score above the national average of 18. Given your results from part D, do you believe that there is evidence that the mean ACT score at this high school is greater than 18? Explain your reasoning.

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