IXL - Find probabilities using the normal distribution II (Algebra 2 practice)

is a normally distributed random variable with mean 48 and standard deviation 21.

What is the probability that

is between 16 and 80?

Write your answer as a decimal rounded to the nearest thousandth.

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Learn with an example

question

is a normally distributed random variable with mean 65 and standard deviation 4.

What is the probability that

is between 60 and 70?

Write your answer as a decimal rounded to the nearest thousandth.

key idea

A random variable with a normal distribution is called normally

distributed.

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.

-value

is a specific value of

solution

Use the random variable

–

𝜇

𝜎

Since

is normally distributed,

has the standard normal distribution.

To find the probability that

is between 60 and 70, first find the

-values

that correspond to the

values of 60 and 70. Call them

and

Then, find the probability that

is between

and

Find the

-values,

and

Use the equation

–

𝜇

𝜎

Plug each value of

into the equation along with

𝜇

and

𝜎

–

𝜇

𝜎

–

1.25

–

𝜇

𝜎

–

1.25

The two

-values

are

–

1.25

and

1.25

Find the probability that

is between

and

Since

is a standard normal variable, use a calculator to find the probability that it is between

–

1.25

and 1.25.

(

–

1.25

)

0.788700…

≈

Round to the nearest thousandth

0.789

Round to the nearest thousandth

So,

(

)

(

–

1.25

)

≈

0.789

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