Answer:
The estimate of a range of plausible values for the true proportion of people that will not wait more than one minute on hold at a 95% confidence level is
Confidence interval = (549.404, 610.596)
Step-by-step explanation:
We will be finding the confidence interval at 95% confidence level.
The proportion of people that hang up the phone in the first minute of waiting
= P = (580/1000) = 0.58
We can then calculate the standard deviation of the distribution of sample means = σₓ = √[np(1-p)]
where n = sample size = 1000
σₓ = √[np(1-p)] = √[1000×0.58×0.42] = 15.61
Confidence interval = (Sample mean) ± (Margin of error)
Sample mean = 580
Margin of Error = (critical value) × (standard deviation of the distribution of sample means)
Critical value = 1.960
Even though we do not have information on the population mean and standard deviation, we can use the z-distribution's z-score for 95% confidence interval instead of the t-distribution's t-score since the sample size is 1000.
Margin of error = 1.960 × 15.61 = 30.596
Confidence interval = (Sample mean) ± (Margin of error)
Confidence interval = 580 ± 30.596
Confidence interval = (549.404, 610.596)
Hope this Helps!!!
