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) n = 1

= 73.0

=  / n = 12.5/ 1=12.5

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

= P(z <0.96 )

Using z table

= 0.8315

part D was right