Question

Assume that females have pulse rates that are normally distributed with a mean of mu equals 72.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts​ (a) through​ (c) below.

(a) If 1 adult female is randomly​ selected, find the probability that her pulse rate is between 66 beats per minute and 78 beats per minute.
The probability is?
(b) If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean between 66 beats per minute and 78 beats per minute
The probability is?
(c) Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

Answer 1

Explanation:

Let X be the pulse rates of females

X is N(72,12.5)

a) P(66<x<78) = P(|Z|<6/12.5)

= P(|Z|<0.48) = 2*.1844=0.3688

b) Each person is independent of the other

Hence P(4*66<4x<4*78) = P(|Z|<24/50) =0.3688^4

c) Because parent distribution is normal