Answer the following questions.

Question

In introductory statistics courses at Large State University, the times it takes students to complete their final exams are normally distributed with a mean of 𝜇 = 92 minutes and a standard deviation of 𝜎 = 14 minutes. Use the figure below to answer the following questions.

Area Under

(a)

Estimate the probability that a randomly selected student will complete their final exam in less than 78 minutes.

 

(b)

The final exam is scheduled to allow 2 hours. Estimate the probability that a randomly selected student will need more than 2 hours to complete their exam.

 

(c)

In a section with 120 students, how many students do you expect will need more than 2 hours to complete their exams?

 students

Answer 1

Hi Tamera,

(a) Looking at the figure, 78 is exactly one standard deviation below the mean 92. That means you want all students who fall below that mark on the figure, Add up every area greater than one standard deviation to the left: 13.5 + 2.35 + 0.15 = 16%

(b) Two hours=120 minutes. 120=92 + 2(14). In other words, students who take two hours will be two standard deviations above the mean 92 minutes. That means we want all areas in the graph greater than mu + 2*sigma:

2.35 + 0.15 = 2.5%

(c) 120*2.5% = 120 * 0.025 = 3 students

I hope this helps.