Question

It is assumed that the test results for a class follow a normal distribution with a mean of 78 and a standard deviation of 36. If you know that a student's grade is greater than 72, what is the probability that it is greater than 84

Answer 1

Answer: 0.4337

Explanation:

Let X represents the test results for a class that follow a normal distribution .

Given: Mean
`\mu=78`, Standard deviation
`\sigma=36`

Then, the probability that it is greater than 84 will be

`P(X>84)=P((X-\mu)/(\sigma)>(84-78)/(36))\\\\=P(Z>0.167)\ \ \ [Z=(X-\mu)/(\sigma)]\\\\=1-P(Z<0.167)\\\\=1-0.5663=0.4337\ [\text{By p-value table}]`

Hence, the required probability = 0.4337