Question

Assume that blood pressure readings are normally distributed with a mean of 124124 and a standard deviation of 9.69.6. If 144144 people are randomly​ selected, find the probability that their mean blood pressure will be less than 126126.

Answer 1

Probability that their mean blood pressure will be less than 126 is 0.9938.

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
`\bar X` = mean blood pressure

So,
`\bar X` ~ N(
`\mu= 124, s.d. = (9.6)/(√(144) )`)

The z score probability distribution for sample mean is given by;

Z =
`(\bar X-\mu)/((\sigma)/(√(n) ) )` ~ N(0,1)

where,
`\mu` = population mean

`\sigma` = population standard deviation

n = sample size = 144

So, probability that their mean blood pressure will be less than 126 is given by = P(
`\bar X` < 126)

P(
`\bar X` < 126) = P(
`(\bar X-\mu)/((\sigma)/(√(n) ) )` <
`(126-124)/((9.6)/(√(144) ) )` ) = P(Z < 2.50) = 0.9938 {using z table}

Therefore, probability that their mean blood pressure will be less than 126 is 0.9938 .