Answer:
Probability that the average pulse of the 100 adults is between 78 and 81 beats per minute is 0.7493.
Step-by-step explanation:
We are given that adult between the age of 21 and 65 have a mean pulse of 80 beats per minute with a standard deviation of 12 beats per minute.
A doctor measures 100 random, independent adults between the ages of 21 and 65 from the population of such adults and calculates their average pulse.
<u>Let</u><u><em> </em></u><u><em> = sample average pulse</em></u>
The z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean pulse = 80 beats per minute
= standard deviation = 12 beats per minute
n = sample of adults measured = 100
Now, probability that the average pulse of the 100 adults is between 78 and 81 beats per minute is given by = P(78 < < 81)
P(78 < < 81) = P( < 81) - P( 78)
P( < 81) = P( < ) = P(Z < 0.83) = 0.79673
P( 78) = P( ) = P(Z -1.67) = 1 - P(Z < 1.67)
= 1 - 0.95254 = 0.04746
Therefore, P(78 < < 81) = 0.79673 - 0.04746 = <u>0.7493</u>