1. A test of reading ability has a population mean of 75 and a standard deviation...

1. A test of reading ability has a population mean of 75 and a standard deviation of 10 when given to third-graders. The distribution is known to be approximately normally distributed.

a. What is the probability that a student will score above a 90? Show your calculation.

b. What test score corresponds to the 25th percentile? Show your calculation.

Say that you selected a random sample of 40 third-grade students from this population.

c. What is the probability that the sample mean of the 40 scores will be greater than 90? Show your calculation.

d. Explain, in one or two sentences, why the result you calculated in part a differs from the result you calculated in part c.

Expert Solution

d. The result we calculated in part a differs from the result in part c because the standard deviation for the sample mean is very less as compared to the standard deviation of X due to which the observations are more concentrated around the population mean as compared to the distribution of X.

orchestra answered 1 year ago

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