Question

A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100. You scored a 625. Calculate your z-score to the nearest hundredth (i.e. 2 decimal places).

z=

Answer 1

Answer: 1.25

Explanation:

Given: A college-entrance exam is designed so that scores are normally distributed with a mean
`(\mu)` = 500 and a standard deviation
`(\sigma)` = 100.

A z-score measures how many standard deviations a given measurement deviates from the mean.

Let Y be a random variable that denotes the scores in the exam.

Formula for z-score =
`(Y-\mu)/(\sigma)`

Z-score =
`(625-500)/(100)`

⇒ Z-score =
`(125)/(100)`

⇒Z-score =1.25

Therefore , the required z-score = 1.25