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 %

Step-by-step 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 : $z=\dfrac{x-\mu}{\sigma}$

For x= 476

$z=\dfrac{476 -476 }{85}=0$

For x= 646

$z=\dfrac{646 -476 }{85}=2$

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

$P(476$

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