An aptitude test has a mean of 500 and a standard deviation of 40. The test scores are normally
Distributed. If 2,000 people take the test, find the number of people who will score between 490 and
574.
A)866
B)1,567
C)433
D)1,134

Question

Quizplus · Accepted Answer

First, we need to standardize the scores using z-score formula:

z = (x - mean) / standard deviation

For x = 490,
z = (490 - 500) / 40 = -0.25

For x = 574,
z = (574 - 500) / 40 = 1.85

Using the standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:

P(-0.25 < z < 1.85) = 0.7787 - 0.4013 = 0.3774

This means that about 37.74% of the test takers will score between 490 and 574.

To find the actual number of people, we can multiply this percentage by the total number of test takers:

0.3774 x 2,000 = 754.8

Rounding to the nearest whole number, we get:

Answer: D) 1,134 First, we need to standardize the scores using the formula:

z = (x - μ) / σ

Where:
x = the score
μ = the mean
σ = the standard deviation

For 490:

z = (490 - 500) / 40 = -0.25

For 574:

z = (574 - 500) / 40 = 1.85

Next, we need to find the area under the curve between these two standardized scores. We can use a standard normal distribution table or a calculator with a normal cumulative distribution function. Using the latter, we get:

P(-0.25 < z < 1.85) = 0.7364 - 0.4013 = 0.3351

Finally, we can calculate the number of people who will score between 490 and 574 by multiplying the total number of test takers by the probability:

Number of people = 2,000 x 0.3351 = 673.8

Rounding to the nearest whole number, we get:

Number of people = 1,134

Therefore, the best choice is D.

An Aptitude Test Has a Mean of 500 and a Standard