Question

Suppose the systolic blood pressure of young adults is normally distributed with mean 120 and standard deviation 11.

(a) Find the 77th percentile of this distribution.

(b) Find the probability that a random young adult has systolic blood pressure above 135.

(c) Find the probability that a random young adult has systolic blood pressure within 3.3 standard deviations of the mean.

(d) Suppose you take a sample of 8 young adults and measure their average systolic blood pressure. Carefully jus- tify whether the Central Limit Theorem applies, and if it does, find the probability that the average blood pressure is between 115 and 123.

Answer 1

Let X denote the systolic blood pressure of young adults. Then

a)

We want to find 'x' such that

b)

c)

Required probability =

d)

Since the population distribution is normal, so CLT is applicable.

Using Central Limit theorem, we know,

Required probability =