Question

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

98.21degrees°F

and a standard deviation of

0.66 degrees°F.

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

a.	What is the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the​ mean, or between 97.5.degrees°F and 98.87 degrees°​F?
b.	What is the approximate percentage of healthy adults with body temperatures between 96.23 degrees°F and 100.19 degrees°​F?

a. Approximately

what ​%

of healthy adults in this group have body temperatures within 1 standard deviation of the mean 97.55 and 98.87

11

standard

deviationdeviation

of the​ mean, or between

97.5597.55degrees°F

and

98.8798.87degrees°F.

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

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

98.2198.21degrees°F

and a standard deviation of

0.660.66degrees°F.

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

a.	What is the approximate percentage of healthy adults with body temperatures within 11 standard deviationdeviation of the​ mean, or between 97.5597.55degrees°F and 98.8798.87degrees°​F?
b.	What is the approximate percentage of healthy adults with body temperatures between 96.2396.23degrees°F and 100.19100.19degrees°​F?

a. Approximately

nothing ​%

of healthy adults in this group have body temperatures within

11

standard

deviationdeviation

of the​ mean, or between

97.5597.55degrees°F

and

98.8798.87degrees°F.

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

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

98.2198.21degrees°F

and a standard deviation of

0.660.66degrees°F.

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

a.	What is the approximate percentage of healthy adults with body temperatures within 11 standard deviationdeviation of the​ mean, or between 97.5597.55degrees°F and 98.8798.87degrees°​F?
b.	What is the approximate percentage of healthy adults with body temperatures between 96.2396.23degrees°F and 100.19100.19degrees°​F?

a. Approximately

nothing ​%

of healthy adults in this group have body temperatures within

11

standard

deviationdeviation

of the​ mean, or between

97.5597.55degrees°F

and

98.8798.87degrees°F.

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

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

98.2198.21degrees°F

and a standard deviation of

0.660.66degrees°F.

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

a.	What is the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the​ mean, or between 97.5597.55degrees°F and 98.8798.87degrees°​F?
b.	What is the approximate percentage of healthy adults with body temperatures between 96.2396.23degrees°F and 100.19100.19degrees°​F?

a. Approximately

nothing ​%

of healthy adults in this group have body temperatures within

11

standard

deviationdeviation

of the​ mean, or between

97.5597.55degrees°F

and

98.8798.87degrees°F.

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

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

98.2198.21degrees°F

and a standard deviation of

0.660.66degrees°F.

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

a.	What is the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the​ mean, or between 97.5.degrees°F and 98.87 degrees°​F?
b.	What is the approximate percentage of healthy adults with body temperatures between 96.23 degrees°F and 100.19 degrees°​F?

a. Approximately

nothing ​%

of healthy adults in this group have body temperatures within

11

standard

deviation

of the​ mean, or between

97.55.55degrees°F

and

98.87 degrees°F.

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

Answer 1

=Mean= 98.21
=standard deviation = 0.66

a. Approximately what ​% of healthy adults in this group have body temperatures within 1 standard deviation of the mean or between 97.55 and 98.87

Answer :

We have to calculate

p( 97.55 < X < 98.87)

using standard normal distribution

p( (97.55-98.21)/0.66  < (X -)/< (98.87-98.21)/0.66)

=p(-1 < Z <1)

=p(Z<3) - p(Z<-3)

=0.8413 -0.1586

=0.6828

=68.28%

b.

What is the approximate percentage of healthy adults with body temperatures between 96.23 degrees°F and 100.19 degrees°​F?

We have to calculate

p( 96.23 < X < 100.19)

using standard normal distribution

p( (96.23-98.21)/0.66  < (X -)/< (100.19-98.21)/0.66)

=p(-3 < Z <3)

=p(Z<3) - p(Z<-3)

=0.9986 - 0.00135

=0.9973

=99.73%

Answer

a) Approximately 68.28 ​% of healthy adults in this group have body temperatures within 1 standard deviation of the mean or between 97.55 and 98.87

b) Approximate 99.73 % percentage of healthy adults with body temperatures between 96.23 degrees°F and 100.19 degrees°​F