Question

1. X ~ N(60, 11). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums. Find the 30th percentile. (Round your answer to two decimal places.)

2. X ~ N(50, 12). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums. Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(48 < X < 54) =

3.X ~ N(70, 12). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums. Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(36 < X < 66) =

4.Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 254 feet and a standard deviation of 58 feet. We randomly sample 49 fly balls.

A) What is the probability that the 49 balls traveled an average of less than 246 feet? (Round your answer to four decimal places.).Find the 80th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)

B) Find the 80th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)

Answer 1

Questions are answered below.