Assume that females have pulse rates that are normally distributed with a mean o
ID: 3338660 • Letter: A
Question
Assume that females have pulse rates that are normally distributed with a mean of
mu equals 73.0=73.0
beats per minute and a standard deviation of
sigma equals 12.5=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
76
beats per minute.The probability is
nothing.
(Round to four decimal places as needed.)
b. If
25
adult females are randomly selected, find the probability that they have pulse rates with a mean less than
76
beats per minute.The probability is
nothing.
(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 mean pulse rate exceeds 30, 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 distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.
D.
Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.
Explanation / Answer
Mean is 73 and s is 12.5. z is given as (x-mean)/s
a) P(x<76)=P(z<(76-73)/12.5)=P(z<0.24), from normal distribution table we get 0.5948
b) P(x<75)=P(z<(76-73)/(12.5/sqrt(25)))=P(z<1.2) , from normal distribution table we get 0.8849
c) Answer is D