Question

20000 students took a standardized math test. The scores on the test are normally distributed, with a mean score of 85 and a standard deviation of 5. About how many students scored between 90 and 95?

Answer 1

Answer: 2718

Explanation:

Given: Mean score = 85

Standard deviation = 5

Let x be the score of a random student that follows normal distribution.

Then, the probability that a student scored between 90 and 95 will be

`P(90< x < 95)\\\\=P((90-85)/(5)<(x-\mu)/(\sigma)<(95-85)/(5))\\\\= P(1< z< 2)\ \ \ \ \ [z=(x-\mu)/(\sigma)]\\\\=P(z<2)-P(z<1)\\\\=0.9772-0.8413\\\\=0.1359`

The number of students scored between 90 and 95 = 0.1359 x (Total students)

= 0.1359 (20000)

= 2718

Hence, The number of students scored between 90 and 95 = 2718