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.

$z=\frac{x-\mu}{\sigma}$, where,        

z = z-score,

x = Random sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

$z=\frac{77-74}{3}$

$z=\frac{3}{3}$

$z=1$

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

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

$P(z>1)=1-P(z$

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.