## Question 370:

1

Calculate the z-scores or standardized values by subtracting each value from the mean, then dividing that result by the standard deviation.

1. 29 hours z-score = (29-32)/2 = -1.5
2. 34 hours z-score = (34-32)/2 = 1

For the last part, you need to find the are under the normal curve between the z-scores corresponding to 32 and 34 hours. First we find the z-score for 32. Since it is the same as the mean, it has a z-score of 0 (32-32)/2 = 0. We already found the z-score for 34 hours above as a z-score of 1. To find the area between these two values we simply subtract the larger from the smaller to find the standardized area in between (1-0) = 1. We now simply lookup the area under the normal curve corresponding to a z-score of 1 using the z-score to percentile calculator (select 1-sided area). You should get area of 84%. In other words, we'd expect 84% of garages to take between 32 and 34 hours.

You can visualize this relationship by looking at the interactive graph of the standard normal curve. Enter the mean of 29 and standard deviation of 2 in the 1-sided area graph to see this relationship.