Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Use technology or a z-score table to answer the question.

The average balance at a credit union is normally distributed with a mean of $240 and a standard deviation of $100. Joe's balance is $260.

What percent of all accounts at the credit union have a balance less than Joe's?

Round your answer to the nearest whole number.

Answer 1

Answer:  b) 58%

Step-by-step explanation:

First, let's find the z-score using the formula: $z=\dfrac{x-\mu}{\sigma}$

$z=\dfrac{260-240}{100}=\dfrac{20}{100}=\boxed{0.20}$

Next, refer to the z-score table below to find the value of 0.20

Look on the left side for 0.20 and the top for 0.00 to find the percent for 0.20.  The table shows the percent above the MEAN so you need to add the percent below the mean (50%) to the value in the table.

  0.0793

+ 0.5      

  0.5793    = 57.93%

Answer 2

The percent of accounts at the credit union with a balance less than Joe's balance is 58%. Hence, we take the second option.

What is a Z-score?

A Z-score is a numerical measurement that describes the relationship between a value and the mean of a set of values. The standard deviations from the mean are used to calculate the Z-score. When a Z-score is zero, it means the data point's score is the same as the mean score.

How is a z-score calculated?

The Z-score is calculated using the formula:

z = (x - μ)/σ,

where z: standard score, x: observed value, μ: mean of the sample,

and σ: standard deviation of the sample.

How do we solve the given question?

We are given the mean μ = $240 and the standard deviation σ = $100 of the average balance at a credit union.

We are asked to find what percent of all accounts at the credit union have a balance less than Joe's account.

To find it, we first calculate the z-score of Joe's balance x = $260.

z = (x - μ)/σ

or, z = (260 - 240)/100 = 0.2.

Using the table of z-score, we find the value of the distribution below the z-score of Joe = 0.2.

We take the value at the intersection of 0.2 and 0.00, which is, 0.5793.

∴ The percent of accounts at the credit union with a balance less than Joe's balance = 0.5793*100% = 57.93% ≈ 58%. (second option)

Learn more about z-score at

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