Answer:
Probability that their mean blood pressure will be less than 126 is 0.9938.
Step-by-step explanation:
We are given that blood pressure readings are normally distributed with a mean of 124 and a standard deviation of 9.6. Also, 144 people are randomly selected.
Let [tex]\bar X[/tex] = mean blood pressure
So, [tex]\bar X[/tex] ~ N( [tex]\mu= 124, s.d. = \frac{9.6}{\sqrt{144} }[/tex])
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean
[tex]\sigma[/tex] = population standard deviation
n = sample size = 144
So, probability that their mean blood pressure will be less than 126 is given by = P([tex]\bar X[/tex] < 126)
P([tex]\bar X[/tex] < 126) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{126-124}{\frac{9.6}{\sqrt{144} } }[/tex] ) = P(Z < 2.50) = 0.9938 {using z table}
Therefore, probability that their mean blood pressure will be less than 126 is 0.9938 .
