Question

The distribution of time needed to complete a certain programming task is approximately normal, with mean 47 minutes and standard deviation 6 minutes. What is the probability that a randomly chosen task will take less than 34 minutes or more than 60 minutes to complete?

Answer 1

Answer:

the probability that a randomly chosen task will take less than 34 minutes or more than 60 minutes to complete is 0.03

Step-by-step explanation:

To identify the probability that a randomly chosen task will take less than 34 minutes or more than 60 minutes to complete, we need to calculate z-score and p-values of the 34 min. and 60 min.

That is P(X<34) + P(X>60)=P(z<z(34)) + P(z>z(60))

z score can be calculated using the formula

z=$\frac{X-M}{s}$ where

• X is the value we are looking for its z-score (34,60)

• M is the mean time to complete a certain programming task (47 min.)

• s is the standard deviation (6 min.)

Then z-score of 34 min is:

z(34)=$\frac{34-47}{6}$ ≈ -2.17

and P(z<z(34)) =0.015

z-score of 60 min is:

z(34)=$\frac{60-47}{6}$ ≈ 2.17

and P(z<z(60)) =0.985, P(z>z(60)) = 1-0.985=0.015

Thus

the probability that a randomly chosen task will take less than 34 minutes or more than 60 minutes to complete is 0.015+0.015=0.03