Question

The average grade in a statistics course has been 71 with a standard deviation of 10.5. If a random sample of 60 is selected from this population, what is the probability that the average grade is more than 75? (Round your z-value to 2 decimal places and the final answer to 4 decimal places)

Probability= ________

Answer 1

Population mean, = 71

Standard deviation, = 10.5

Sample size, n = 60

According to Central Limit Theorem, the distribution of sample mean, is approximately normal.

P( < A) = P(Z < (A - )/)

= = 71

=

=

= 1.356

P(average grade is more than 75), P( > 75)

= 1 - P( < 75)

= 1 - P(Z < (75 - 71)/1.356)

= 1 - P(Z < 2.95)

= 1 - 0.9984

= 0.0016