Central Limit Theorem 7.0

Question

A population of values has a normal distribution with  and . You intend to draw a random sample of size .

Find P, which is the mean separating the bottom 83% means from the top 17% means.P (for sample means) = 

Enter your answers as numbers accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

For a sample mean P, z-score = (P - population mean)/(standard deviation/square root of sample size).

First find the z-score associated with the 83rd percentile (look up z-score corresponding to 0.83 probability), which 0.954.

Using given population mean (85), standard deviation (33.8), sample size (25) and computed z-score (0.954), you can plug those values into the z-score equation and solve for the associated sample mean P:

0.954 = (P - 85)/(33.8/sqrt(25))

0.954 = (P - 85)/6.76

6.45 = P - 85

P = 91.45 ~ 91.5