Answer: (122.52, 133.88)
Step-by-step explanation:
We are to construct a 99% confidence interval for population mean time.
From our question, we have the following parameters
Sample size (n) = 128
Sample mean (x) = 128.2
Sample standard deviation (s) = 24.9
To construct a 99% confidence interval, we use the formulae below.
u = x + Zα/2 × s/√n........ For upper limit
u = x - Zα/2 × s/√n........ For lower limit
We are using a z score for our critical value (Zα/2) and that's because our sample size is greater than 30 (n = 128), even though we have our sample standard deviation.
The value of Zα/2 is gotten using a z distribution table and has a value of 2.58
For lower limit, we have that
u = 128.2 - 2.58/ (24.9/√128)
u = 128.2 - 2.58 (2.2)
u = 128.2 - 5.678
u = 122.52.
For upper limit, we have that
u = 128.2 + 2.58/ (24.9/√128)
u = 128.2 + 2.58 (2.2)
u = 128.2 + 5.678
u = 133.88
Hence the 99% confidence interval for the mean amount of time customer stays is (122.52, 133.88)
