SOLUTION: The mean pulse rate for adults is 72 beats per minute (www.healthepic.com) and let’s suppose that the standard deviation is 9 bpm. Find: a. The probability that a randomly ch

Question 1204474: The mean pulse rate for adults is 72 beats per minute (www.healthepic.com) and let’s suppose that the standard deviation is 9 bpm. Find:
a. The probability that a randomly chosen adult has a pulse rate over 77 bpm assuming that the rates are normally distributed.
b. The probability that a random sample of 18 adults will have a mean beats per minute over 77

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mean is 72 beats per minute.
standard deviation is 9 beats per minute (supposed).

probabiiity that a random person has over 77 beats per minue = .2893.

probbility that the mean of a random sample has over 77 beats per minute = .0092.

here are the resuts, using the calculator at https://davidmlane.com/hyperstat/z_table.html

the differnce is that, for an individual sample, the standard deviation is used, while for the mean of a random sample, the standard error is used.

standard error = standard deviation / square root of sample size = 9 / sqrt(18) = 2.1213.

the standard error is defined as the standard deviation of the distribution of sample means.
this is different than the distribution of individual samples.
as the size of the sample gets larger, the standard error gets smaller.

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