Question

Suppose the test scores on a final exam are normally distributed with a mean of 74 and a standard deviation of 3. What is the probability that a randomly selected test has a score higher than 77?

Answer 1

We have been given that the test scores on a final exam are normally distributed with a mean of 74 and a standard deviation of 3. We are asked to find the probability that a randomly selected test has a score higher than 77.

First of all, we will find z-score corresponding to sample score 77.

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

z = z-score,

x = Random sample score,

`\mu` = Mean,

`\sigma` = Standard deviation.

`z=(77-74)/(3)`

`z=(3)/(3)`

`z=1`

Now we need to find
`P(z>1)`.

We will use formula
`P(z>a)=1-P(z<a)` to find the probability greater than a z-score of 1.

`P(z>1)=1-P(z<1)`

Using normal distribution table, we will get:

`P(z>1)=1-0.84134`

`P(z>1)=0.15866`

Therefore, the probability that a randomly selected test has a score higher than 77 would be 0.15866.