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

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