Question

The test grades of a science class are given.

78, 75, 70, 92, 69, 83, 98, 76, 75, 82, 91, 89

The grades are normally distributed with a mean of 81.5 and a standard deviation of 9.3.



What is the z-score of the highest grade in the test?

Round the answer to the nearest hundredth.

Answer 1

Answer:

1.77 to nearest hundredth

Step-by-step explanation:

Z-score = (score - mean)  / standard deviation

98 is the highest score and its z-score is (98- 81.5) / 9.3

= 1.7742

Answer 2

Answer: 1.77

Step-by-step explanation:

Given : The test grades of a science class are given.

78, 75, 70, 92, 69, 83, 98, 76, 75, 82, 91, 89

The grades are normally distributed with a mean $\mu= 81.5$ and a standard deviation $\sigma=9.3$ .

let x be any random variable represents the test grades of a science class.

Formula for z-score:-

$z=\dfrac{x-\mu}{\sigma}$

The highest score= 98

Then , the z-score of the highest grade in the test will be :-

$z=\dfrac{98-81.5}{9.3}=1.77419354839\approx1.77$

Hence, the z-score of the highest grade in the test =1.77