Question

We know that the number of books owned by the population of Gonzaga University students follows a normal distribution and has a mean of 32 and a standard deviation of 3.8. Show all work for full credit! Find the probability that a single randomly selected student owns more than 34 books. Find the probability that a sample of size 40 is randomly selected with a mean that is larger than 34 books.

Answer 1

This is a normal distribution question with

22 Mean(x) = 32 Standard Deviation(o) = 3.8 Since we know that score =-

a) P(x > 34.0)=?
The z-score at x = 34.0 is,

34.0-32.0 3.8

z = 0.5263
This implies that
P(x > 34.0) = P(z > 0.5263) = 1 - 0.7007
P(x > 34.0) = 0.2993

b) Sample size (n) = 40
Since we know that

Sample mean(T) =#= 32.0 Sample standard deviation(s) = = 0.6008 Vn Zscore = 2 –

P(x > 34.0)=?
The z-score at x = 34.0 is,

34.0-32.0 0,6008

z = 3.3289
This implies that
P(x > 34.0) = P(z > 3.3289) = 1 - 0.9996
P(x > 34.0) = 0.0004
PS: you have to refer z score table to find the final probabilities.
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