Question

The scores of an entrance exam for a high school in a particular year were bell-shaped in nature. If the mean and standard deviation were 350 and 50 respectively, then:

Answer 1

P(200 ≤ X ≤ 500) = 0.9973

Explanation:

Let assume that the question intends us to find what percentage of students scored between 500 and 200 on this test.

Given that:

`\mu = 350 \\ \\ \sigma = 50 \\ \\ x_ 1 =200 \\ \\ x_2 = 500`

We need to first compute the Z test statistics

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

`z_1 = (200 - 350)/(50)= -3`

`z_2= (500 - 350)/(50)= 3`

Thus;

`P(200 \le X \le 500) = P(-3 \le z \le 3) \\ \\= P(z \le 3) - P(z \le -3) \\ \\= 0.9987 - 0.0014 \\ \\ = 0.9973`