The total study time for a statistics assignment in a population of college stud

Question

The total study time for a statistics assignment in a population of college students was approximately Normally distributed with a mean of 14.32 hours and standard deviation of 5.64 hours. Suppose you plan to take an SRS of size 40 and compute the average study time.

What is the mean and standard deviation of your sample?

What is the probability of coming up with a sample that shows that they studied 10 hours or less? (Nothing too complicated in this question – it is simply intended as a review of using your z-table).

Please type your steps out for readibility and so I can understand without the use of software (like Excel). Thanks!

Explanation / Answer

Mean µ =14.32

Standard deviations () =5.64

Sample size (n) =40

Standard error(SE) = /sqrt(n) = 5.64/Sqrt(40)

                        SE =0.8918

P(x 10) = P(z < ( x-µ)/SE)

                        =P(z < (10-14.32)/0.8918)

                        =P(z< -4.8441)

                        =0.0000 from the standard norman table

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