Let X denote the time in hours needed to locate and correct a problem in the software that governs the timing of traffic lights in the downtown area of a large city. Assume that X is normally distributed with mean 10 hours and variance 9.

Question

(a) Find the probability that the next problem will require at most 15 hours to find and correct.

(b) The fastest 5% of repairs take at most how many hours to complete?

How do we do part b only using standard normal table?

Answer 1

standard deviation is the √ of the variance

the fastest 5% are more than 2 s.d. below the mean

Answer 2

How do we get that : 2 s.d below mean?

Answer 3

sorry ... my mistake
... approx. 95% of the population lies within 2 s.d. of the mean
... but we want the bottom 5%

s.d. = √(variance) = √9 = 3

looking at a z-score table
... the bottom 5% is approx. 1.64 s.d. below the mean

1.64 * 3 hr =?