IXL - Find values of normal variables (Precalculus practice)

Complete the statement. Round your answer to the nearest thousandth.

In a population that is normally distributed with mean 88 and standard deviation 14, the bottom

of the values are those less than

ref_doc_title.

Learn with an example

question

Complete the statement. Round your answer to the nearest thousandth.

In a population that is normally distributed with mean 41 and standard deviation 13, the bottom

of the values are those less than

key idea

A random variable with a normal distribution is said to be normally

distributed.

A normal distribution is symmetric around the mean.

The standard normal distribution is the normal distribution with mean 0 and standard deviation 1. A random variable with the standard normal distribution is called a standard normal

variable.

is a normally distributed random variable with mean

𝜇

and standard deviation

𝜎

then the distribution of

–

𝜇

𝜎

is the standard normal distribution.

For a specific value

–

𝜇

𝜎

is called the

-value

is a specific value of

solution

Let

be a random variable with the same distribution as the population. So,

is normally distributed with mean

𝜇

and standard deviation

𝜎

You want to find the value

such that

(

)

This corresponds to the bottom

of the values in population.

60%

To find

use the random variable:

–

𝜇

𝜎

–

Since

is normally distributed,

has the standard normal distribution.

Find the

-value

corresponding to the probability

(

)

0.6

Call it

Then, use

to solve for

(Most calculators are set up to find

-values

rather than

-values.)

Find

Use a calculator to find the value

such that

(

)

0.6

(

0.253347…

)

0.6

So,

0.253347…

Find

–

0.253347…

–

3.293512…

–

44.293512…

State the answer.

To the nearest thousandth, the bottom

of the values are those less than 44.294.

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Not feeling ready yet? These can help:

EE.5Find z-values

C.8Solve two-step linear equations

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