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Human body temperatures are normally distributed with a mean of 98.20 degrees Fahrenheit and a standard deviation of 0.62 degrees Fahrenheit. Find the temperature that separates the top 7% from the bottom 93%.

Please explain!

Sagot :

[tex] 99.12[/tex] is the answer.

Step-by-step Explanation:

To find- Probability area bound by 93% or 0.93.

Steps-

0.5 lies to the lie of the mean value.

→ 0.93 - 0.5 = 0.43 lies to the right of the mean.

Now find the corresponding "z" value for 0.43

It is 1.48.

Use this value to determine the requix value.

You have to use the formula -

[tex]z = x - μσ[/tex]

Solve it for [tex]x[/tex]:-

[tex]x = z \times σ + μ[/tex]

Where;

[tex]x = ? \\ z = 1.48 \\ σ = 0.62 \\ μ = 98.20[/tex]

Now put these values in the

formula;

[tex]x = (1.48 \times 0.62) + 98.20[/tex]

[tex] = > 0.9176+98.20[/tex]

[tex] = > 99.1176[/tex]

[tex] = > 99.12[/tex]

Hence, the temperature that separates

top 7% from the bottom 93%

is 99.12.

Answer:

The temperature that separates the top 7% with the bottom 93% is 99.12 degrees.

Step-by-step explanation:

  • The z-score that corresponds to 93% is about 1.48

(x - 98.2) / 0.62 = 1.48

x - 98.2 = 0.9176

x = 99.12 degrees

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