Question

Sarah is taking a test. The test is designed to produce an overall mean score of 85 with a standard deviation of 5 for all test takers.

Suppose Sarah scored a 90 on the test. Given that the data is approximately normal, standardize the test score and find the area

under the normal curve below the standardized test score

A.

The area below the standardized test score is 0.504

B.

The area below the standardized test score is 0.1587

C.

The area below the standardized test score is 1

D.

The area below the standardized test score is 0.8413

Answer 1

Option D)

The area below the standardized test score is 0.8413

Explanation:

We are given the following information in the question:

Mean, μ = 85

Standard Deviation, σ = 5

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(score is below 90)

`P( x < 90) = P( z < \displaystyle(90 - 85)/(5)) = P(z < 1)`

Calculation the value from standard normal z table, we have,

`P(x < 90) =0.8413 = 84.13\%`

Thus, the correct answer is

Option D)

The area below the standardized test score is 0.8413