Question

Assume that blood pressure readings are normally distributed with a mean of 123 and a population standard deviation of 9.6. If 67 people are randomly selected, find the probability that their mean blood pressure will be less than 125.

Answer 1

Let X be the blood pressure readings                          
X ~ Normal distribution with                           
mean    μ = 123   and standard deviation        σ = 9.6          
n = 67   …Sample size                      

As per Central Limit Theorem, for any distribution with mean μ and standard deviation σ, as the sample size increases, the sampling distribution of the mean, X-bar, can be approximated by a normal distribution with mean µ and standard deviation σ/√n where n is the sample size         

Thus the sample mean X̅ follows Normal Distribution with                           
mean    μ = 123   and standard deviation        σ = 9.6/√67 = 1.1728          
μ = 123                          
σ = 1.1728                          
To find                          
P(mean blood pressure will be less than 125)                          
that is to find P( X̅ < 125)                          
We use Standard Normal Tables or Excel function NORM.DIST to find the probabilities                          
            = NORM.DIST(125, 123, 1.1728, TRUE)                          
            = 0.9559                          
                          
P(mean blood pressure will be less than 125) =    

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