Respuesta :
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.
A) The percent of customers receive the service for half-price is; 61.41%
B) The time to make the guaranteed limit is; 26 minutes 12 seconds
What is the p-value of the distribution?
A) We are given;
Population mean; µ = 19
Sample mean; x' = 20
Standard deviation; σ = 3.5
Thus, z-score is;
z = (20 - 19)/3.5
z = 0.29
From online p-value from s-score calculator, the p-value for z = 0.29 is;
p = 0.6141 = 61.41%
B) We are told that they now want more than 2% to get the discount. This means that they want less than 98% or 0.98 getting the discount.
The z-score for 0.98 is; z = 2.055
Thus, using z-score formula, we have;
2.055 = (x' - 19)/3.5
x' - 19 = 3.5 * 2.055
x' - 19 = 7.1925
x' = 26.1925 = 26 minutes 12 seconds
Read more about P-value at; https://brainly.com/question/4621112
