Question

Assume that females have pulse rates that are normally distributed with a mean of mu equals 73.0 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 less than 79 beats per minute. The probability is ___. ​(Round to four decimal places as​ needed.) b. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 79 beats per minute. The probability is ___ ​(Round to four decimal places as​ needed.)

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

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

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

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

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

Answer 1

Solution :

Given that ,

mean = = 73.0

standard deviation = = 12.5

a) P(x < 79) = P[(x - ) / < (79 - 73.0) / 12.5]

= P(z < 0.48)

Using z table,

= 0.6844

b) n = 4

=   = 73.0

= / n = 12.5 / 4 = 6.25

P( < 79) = P(( - ) / < (79 - 73.0) / 6.25)

= P(z < 0.96)

Using z table

= 0.8315

c) correct option is = A.

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