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.

Answer 1

63% of students

Explanation:

Z = (X - μ) / σ

Z = 520 - 500 / 60

Z = 0.33

ON THE Z-TABLE

0.33 = 0.6293

62.93% = 63% of students answer

Answer 2

Subtract the mean from Jake's score:

520 - 500 = 20

No divide that by the standard deviation:

20/60 = 0.33

This means Jake scored 0.33 standard deviations above the mean.

Now using the Z-table find 0.33: 0.33 = 0.6293 = 62.93% of students scored below Jake.

Rounded to nearest whole number = 63%