Question

Tony was diagnosed with high blood pressure. He was able to keep his blood pressure in control for several months by taking a blood pressure drug. During that period, the probability distribution of his systolic blood pressure readings followed a normal distribution with a mean of 127 mm Hg and a standard deviation of 8.3 mm Hg. If he takes 5 readings of his blood pressure:

(a) What are the mean and standard deviation of the sampling distribution of the sample mean blood pressure?

(b) What is the probability that the sample mean blood pressure is between 120 mm Hg and 136 mm Hg?

Answer 1

Solution :

Given that ,

mean =   = 127

standard deviation = =8.3

n = 5

a.

sampling distribution of the sample mean   = 127

sampling distribution of the standard deviation    =  / n= 8.3/ 5=3.71

b.

P(120<     <136 ) = P[(120-127) /3.71 < ( - ) /   < (136-127) /3.71 )]

= P(-1.89 < Z <2.43)

= P(Z <2.43 ) - P(Z <-1.89 )

Using z table

=0.9925 - 0.0294

probability=0.9631