Question

Assume that females have pulse rates that are normally distributed with a mean of u equals 75.0 beats per minute and a standard deviation of

σ=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 less than 82 beats per minute. The probability is ___.

b. If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 82 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?

A. Since the distribution is of sample​ means, not​ individuals, the distribution is a normal distribution for any sample size.

B. Since the mean pulse rate exceeds​ 30, the distribution of sample means is a normal distribution for any sample size.

C. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

D. Since the distribution is of​ individuals, not sample​ means, the distribution is a normal distribution for any sample size.

Answer 1

Solution :

= / n = 12.5 / 25 =  2.5

(a)

P(x < 82) = P[(x - ) / < (82 - 75) / 12.5]

= P(z < 0.56)

= 0.7123

(b)

P( < 82) = P(( - ) / < (82 - 75) / 2.5)

= P(z < 2.8)

= 0.9974

C. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.