00:01
For this question, we are told that the time to complete a construction project is normally distributed with a mean of 60 weeks and a standard deviation of four weeks.
00:13
For part a, we were asked for the probability that the project will be finished in 62 weeks or less.
00:21
So this is the probability that x is no more than 62.
00:26
If this graph represents the normal distribution for the length of time it takes to complete the project, we have the mean of 6 .6.
00:34
60 weeks exactly in the center, standard deviation of 4, 62 is approximately here, and the probability that x is less than or equal to 62 is equal to the area under the curve and to the left of 62.
00:53
So that's the area of this blue shaded region.
00:57
If we want to use a standard normal table to solve this probability, we first standardize the random variable according to this formula.
01:08
That gives us the probability that z is less than or equal to 1.
01:13
And if we look up one half in the standard normal table, that corresponds to a cumulative probability of .6915, it would be the probability that the project will be finished in 66 weeks or less.
01:39
This is the probability that x is less than or equal to 66...