Question

Scores on a recent ACT test yielded mean 20.9 and standard deviation 4.7. find the probability that a random sample of 32 test scores had a mean below 20.

a) .1914
b) .5753
c) .8599
d) .4247
e) .1401

Answer 1

E. 0.1401

Explanation:

The mean here has been given as 20.9

The standard deviation sd = 4.7

Random sample n = 32

Sd/√n

= 4.7/√32

= 0.8309

Probability of x less than 20

= 20-20.9/0.8309

= -0.9/0.8309

= -1.083

P(z<-1.083)

When we go to the z table

= 0.1401

Therefore the probability is 0.1401 and the answer to this question is E.