Question

he body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of

98.06egrees°F

and a standard deviation of

0.69Using the empirical​ rule, find each approximate percentage below.

a.	What is the approximate percentage of healthy adults with body temperatures within 1 standard deviationdeviation of the​ mean, or between 97.3es°F and 98.7598.75degrees°​F?
b.	What is the approximate percentage of healthy adults with body temperatures between 95.9degrees°F and 100.13degrees°​F?

a. Approximately

of healthy adults in this group have body temperatures within

1

standard

deviationdeviation

of the​ mean, or between

97.37degrees°F

and

98.75degrees°F.

​(Type an integer or a decimal. Do not​ round.)

Answer 1

This is a normal distribution question with

a) P(97.3 < x < 98.75)=?

This implies that

P(97.3 < x < 98.75) = P(-1.1014 < z < 1.0) = P(Z < 1.0) - P(Z < -1.1014)

P(97.3 < x < 98.75) = 0.8413447460685429 - 0.13536130272219282

P(97.3 < x < 98.75) = 0.706 = 70.6%

b) P(95.9 < x < 100.13)=?

This implies that

P(95.9 < x < 100.13) = P(-3.1304 < z < 3.0) = P(Z < 3.0) - P(Z < -3.1304)

P(95.9 < x < 100.13) = 0.9986501019683699 - 0.0008728421143538322

P(95.9 < x < 100.13) = 0.9978 = 99.86%

c) P(97.37 < x < 98.75)=?

This implies that

P(97.37 < x < 98.75) = P(-1.0 < z < 1.0) = P(Z < 1.0) - P(Z < -1.0)

P(97.37 < x < 98.75) = 0.8413447460685429 - 0.15865525393145707

P(97.37 < x < 98.75) = 0.6827 =68.27%

PS: you have to refer z score table to find the final probabilities.

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