Question

Suppose the scores of students on a statistics course are normally distributed with a mean of 476 and a standard deviation of 85. What percentage of the students scored between 476 and 646 on the exam? (Give your answer to 3 significant figures.)

Answer 1

Answer: 47.72 %

Explanation:

Given : The scores of students on a statistics course are normally distributed with a mean of
`\mu=476` and a standard deviation of
`\sigma=85`.

Let x be the random variable that represents the scores of students on a statistics course .

z-score :
`z=(x-\mu)/(\sigma)`

For x= 476

`z=(476 -476 )/(85)=0`

For x= 646

`z=(646 -476 )/(85)=2`

Now, the probability of the students scored between 476 and 646 on the exam will be :-

`P(476<X<646)=P(0<z<2)=\\\\P(z<2)-P(z<0)= 0.9772498-0.5= 0.4772498\approx47.72\%`

Hence, the percentage of the students scored between 476 and 646 on the exam = 47.72 %