Assume the mean blood pressure readings is 120 mmHg with a standard deviation of 8 mmHg. If 100 people are randomly selected, find the probability that their mean blood pressure will be greater than 122 mmHg. Note: You must justify the use of the normal distribution. 

 

0.0062

Step-by-step explanation

First, we will justify that this is indeed a normal distribution. We are given a a mean and standard deviation in this problem. Also, high blood pressure fits with a natural phenomena. Most of the natural phenomena are considered normally distributed. And if we try to graph the data, we will probably see a bell shaped graph or a Gaussian distribution with a peak at our mean. Also, it is symmetrical at the mean of the graph.

The formula for normal distribution with a given sample n follows:

(x-mean)/(sd/sqrt(n)) = z-value then use z-table to find probability

Given:

mean = 120

sd = 8

n= 100

P(X>122) = (122-120)/(8/sqrt(100)) = 2.5 = P(Z>2.5) = 0.0062