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. 0.9772b. 0.8413c. 0.5d. 0.1587
Accepted Solution
A:
Answer: b. 0.8413Step-by-step explanation:Given : The average time taken to complete an exam, X, follows a normal probability distribution with [tex]\mu=60\text{ minutes}[/tex] and [tex]\sigma=30\text{ minutes}[/tex] .Then, the probability that a randomly chosen student will take more than 30 minutes to complete the exam will be :-[tex]P(x>30)=P(z>\dfrac{30-60}{30})\ \ [\because\ z=\dfrac{x-\mu}{\sigma} ]\\\\=P(z>-1)=P(z<1)\ \ \ [\because\ P(Z>-z)=P(Z<z)]\\\\= 0.8413[/tex] [using z-value table]Hence, the probability that a randomly chosen student will take more than 30 minutes to complete the exam = 0.8413