Question

The mean ACT test score reported by the college's institutional Research Depart was 20.8, with a standard deviation of 4.8. If all possible random samples of size 40 are taken from this population, determine the following: ( Round all final answers to the nearest tenthousandth)

a) name of the sampling Distribution

b) mean and standard error of the sampling distribution of the mean (use the correct name and symbol for each)

c) percent of sample means for a sample of 40 college students that are greater than 25

d) probability that sample means for samples of size 40 fall between 18 and 22

e) which sample mean can we expect to represent the first quartile

Answer 1

Dear student we can provide you with four subquestion at a time.

a) The sampling distribution is approximately normal, as the sample size is large than 30 and the population standard deviation is given.

b) Mean:

standard error:

c) proportion of the sample means for a sample of 40 college students that are greater than 25 is

percent of sample means for a sample of 40 college students that are greater than 25 = 0

d) probability that sample means for samples of size 40 fall between 18 and 22 =