Question

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions. (a) What is the probability of completing the exam in one hour or less?

Answer 1

Answer:

0.02275

Step-by-step explanation:

We have been given that the time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. We are asked to find the probability of completing the exam in one hour or less.

We know that 1 hour equals 60 minutes. First of all, we will find the z-score corresponding to 60 minutes.  

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

z = z-score,

x = Sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

$z=\frac{60-80}{10}$

$z=\frac{-20}{10}$

$z=-2$

Now, we will use normal distribution table to find area under z-score of $-2$ as:

$P(z< -2)$

$P(z< -2)=0.02275$

Therefore, the probability of completing the exam in one hour or less is 0.02275.