Assume that blood pressure readings are normally distributed with a mean of 124 and a standard deviation of 6.4. If 64 people are randomly selected, find the probability that their mean blood pressure will be less than 126. Round to four decimal places.

99.38%

Step-by-step explanation:

We have that the mean (m) is equal to 124, the standard deviation (sd) 6.4 and the sample size (n) = 64

They ask us for P (x <126)

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 = (126 - 124) / (6.4 / (64 ^ 1/2))

z = 2.5

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

P (z <2.5) = 0.9938

The probability is 99.38%