Question

On average, a laptop computer will last for 3.9 years with a standard deviation of .5 years.

17. Find the percentage of laptop computers with a life of more than 4 years.

18. What percentage of laptop computers will last between 3.5 and 4.5 years?

19. What is the probability that a laptop computer will least less than 3 years?

20. What percentage of laptop computers will differ from the mean by more

         than 1.5 years?

Answer 1

#17.
P(X >= 4) = P(z <= (4 - 3.9)/0.5)
= P(z >= 0.2)
= 1 - 0.5793
= 0.4207

#18.
P(3.5 <= X <= 4.5) = P((4.5 - 3.9)/0.5) <= z <= (4.5 - 3.9)/0.5)
= P(-0.8 <= z <= 1.2) = P(z <= 1.2) - P(z <= -0.8)
= 0.8849 - 0.2119
= 0.673

#19.
P(X <= 3) = P(z <= (3 - 3.9)/0.5)
= P(z <= -1.8)
= 0.0359

#10.
P(2.4 <= X <= 5.4) = P((5.4 - 3.9)/0.5) <= z <= (5.4 - 3.9)/0.5)
= P(-3 <= z <= 3) = P(z <= 3) - P(z <= -3)
= 0.9987 - 0.0013
= 0.9974

required probability = 1 - 0.9974 = 0.0026