Answer:
a. 61.41%
b. 27 minutes
Step-by-step explanation:
a: Find the z-score for the situation.
µ = 19
x-bar = 20
σ = 3.5
z = (20 - 19)/3.5 = 0.29
The p-value for z = 0.29 is 0.6141, so 61.41% of people will get this discount
b: They want no more than 2% to get the discount, so they want less than 98% getting the discount. The z-score for 98% (0.98 as a decimal) is 2.055
*You need to look at the chart and find where 0.98 would be. It's between a z-score of 2.05 and 2.06.
The z-score is 2.055 = (x - 19)/3.5 We are solving for the time for this one. So solve for x...
7.1925 = x - 19 (multiply both sides by 3.5)
26.1925 = x (add 19 to both sides)
So 26.1925 minutes, or about 26 minutes, 12 seconds, so round up to 27 minutes because they want less than 2%. I chose 27 minutes because no places give odd wait times like 26 minutes 12 seconds.