Question

A random sample of 25 observations is to be drawn from a population with the mean of 40 and a standard deviation of 25. The probability that the mean of the sample will exceed 45 is:

a.Not possible to compute

b. 0.4772

c. 0.4207

d. 0.0228

Answer 1

Solution: Here, the given information are

n=25, =40,  =25

The probability that the mean of the sample will exceed 45 is:

P(>45) =1-P(<45) ------------------ P(x>a)=1-P(x<a)

=1- --------------------(using central limit theorem for mean)

=1-P(z<1)

= 1-0.8413-----------(from z table)

=0.1587

The correct option is a) Not possible to compute based on the information provided.