Question

The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 60. Jake scored 520 on the test. Find the percent of students that scored below Jake. Round your answer to the nearest whole number. (Include a step by step description of the process you used to find that percentage.)

*You will need to find the z-score using the z-score formula, the probability using the table, then change the probability to a percent. (Use the z-score table to help answer the question. )

What is the z score?

What is the probability using the table above?

What is the probability written as a percent?

Answer 1

z = 0.33

Explanation:

Mean = u = 500

Standard Deviation = s = 60

Scores of Jake = x = 520

Step 1: Finding the z score

In order to find the percentage who scored below Jake first we have to convert the scores of Jake to z scores. The formula to find z value is:

`z=(x-u)/(s)`

Using the given values in this formula, we get the z scores:

`z=(520-500)/(60)=0.33`

Thus, rounded of to two decimal places, the z-value for Jake's score is 0.33

Step 2: Find probability from the z-table

In the given table, from first column we will find the value 0.3. In the row across 0.3 we will find the value directly below 0.03 as 0.3 + 0.03 = 0.33

This value comes out to be 0.6293

The image attached below shows this process of finding the probability.

Step 3: Converting the probability to percentage

In order to convert this probability to percentage simply multiply it be 100.

So, 0.6293 = 62.93 %

62.93% rounded to nearest whole number will be 63%

This tells us that approximately 63% students scored below Jake i.e. below 520.