Question

One college class had a total of 70 students. The average score for the class on the last exam was 85.2 with a standard deviation of 4.4. A random sample of 32 students was selected. a. Calculate the standard error of the mean. b. What is the probability that the sample mean will be less than 87​? c. What is the probability that the sample mean will be more than 86​? d. What is the probability that the sample mean will be between 84.5 and 86.5​?

Answer 1

(A) standard error of mean =

where sigma = 4.4 and sample size n = 32

(B) Using normalcdf

setting the following values

lower = -999

upper = 87

mean = 85.2

standard error = 0.78

P(Xbar<87) = normalcdf(-999,87,85.2,0.78)

= 0.9895

(C)

Using normalcdf

setting the following values

lower = 86

upper = 99

mean = 85.2

standard error = 0.78

P(Xbar>86) = normalcdf(86,999,85.2,0.78)

= 0.1525

(D)

Using normalcdf

setting the following values

lower = 84.5

upper = 86.5

mean = 85.2

standard error = 0.78

P(84.5<Xbar<86.5) = normalcdf(84.5,86.5,85.2,0.78)

= 0.7675