Question

A sample of size

23

will be drawn from a population with mean

136

and standard deviation

24

.

(a) Is it appropriate to use the normal distribution to find probabilities for

x

?

(b) If appropriate find the probability that

x

will be less than

118

.

(c) If appropriate find the

80th

percentile of

x

.

Answer 1

Solution:

Given, X follows a distribution having

Mean =    = 136

SD =   = 24

We do not know whether this population is normally distributed or not.

A sample of size n = 23 is taken from this population.

Let be the mean of sample.

This sample size is small , because 23 < 30

a)

Is it appropriate to use the normal distribution to find probabilities for ?

NO , Not appropriate

(Sampling distribution of is approximatrly normal if the sample size n > 30 or if the population distribution is normal)