Question

For a sample of n=64​, the probability of a sample mean being less than 20.5 if u = 21 and sigma = 1.31 is ​(Round to four decimal places as​ needed.) Would the given sample mean be considered​ unusual?

Answer 1

Answer:

The mean is usual

Step-by-step explanation:

We have that the mean (m) is equal to 21, the standard deviation (sd) = 1.31 and the sample size (n) = 64

They ask us for P (x <20.5)

For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / (sd / (n ^ 1/2))

We have all these values, replacing we have:

z = (20.5 - 21) / (1.31 / (64 ^ 1/2))

z = -3.05

With the normal distribution table (attached), we have that at that value, the probability is:

P (z <-3.05) = 0.0002

The mean is usual because P (x> 20.5) = 1 - P (x <20.5) = 1 - 0.0002 = 0.9998 is a fairly high probability.