Question

The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes.
What is the probability that a randomly chosen student will take more than 30 minutes to complete the exam?


Select one:


a. 0.9772


b. 0.8413


c. 0.5


d. 0.1587

Answer 1

Answer: b. 0.8413

Step-by-step explanation:

Given : The average time taken to complete an exam, X, follows a normal probability distribution with $\mu=60\text{ minutes}$ and $\sigma=30\text{ minutes}$ .

Then, the  probability that a randomly chosen student will take more than 30 minutes to complete the exam will be :-

$P(x>30)=P(z>\dfrac{30-60}{30})\ \ [\because\ z=\dfrac{x-\mu}{\sigma} ]\\\\=P(z>-1)=P(z-z)=P(Z$

 [using z-value table]

Hence, the probability that a randomly chosen student will take more than 30 minutes to complete the exam =  0.8413