Question

The time for a professor to grade an exam is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes.

1. Compute Z-score if it took the professor 15 minutes to grade an exam

2. What is the probability that a randomly selected exam will require between 12 and 15 minutes to grade?

3. What is the probability that a randomly selected exam will require less than 15 minutes to grade?

Answer 1

Define random variable X :  time for a professor

X is normally distributed with mean = = 12.6 and standard deviation = = 2.5

1)

z score for x = 15

z = 0.96

Z-score if it took the professor 15 minutes to grade = 0.96

2)

Here we have to find P(12 < X < 15)

where z is standard normal variable

= P(z < 0.96) - P(z < -0.24)

= 0.8315 - 0.4052 (From statistical table of z values)

= 0.4263

Probability that a randomly selected will require between 12 and 15 minutes to grade is 0.4263

3)

Here we have to find P(X < 15)

  

  

where z is standard normal variable

= 0.8315 (From statistical table of z values)

Probability that a randomly selected will require less than 15 minutes to grade is 0.8315