Question 1133027: 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?
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 sample means, not individuals, the distribution 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.
Your answer is correct.D.
Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! sigma is the sd
z=(x-mean)/sd
(66-72)/12.5=-0.48
(78-72)/12.5=+0.48
probability of z between those two values is 0.3688
for 4 women
if the question is the mean of their pulses is in this interval, then the standard error is 12.5/sqrt(4) or 6.25
then the z is between -0.96 and +0.96 and the probability is 0.6629.
If the distribution originally is normal, then samples taken from that distribution may be assumed to be normal. The distribution is normal, and four are sampled from that, so they are sampled from a normal distribution. Thirty is not magic, by the way. Ten may be sufficient from a near normal distribution, and fifty may not be sufficient from a skewed distribution.
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