Final answer:
To construct a 99% confidence interval for the number of walk-in customers, use the given sample mean (67.3), standard deviation (7.1), and the sample size (63). With these values, the confidence interval is approximately (65, 70).
Step-by-step explanation:
To construct a 99% confidence interval for the number of walk-in customers on a given day at the restaurant, we can use the sample mean, the sample standard deviation, and the size of the sample. Since the question does not provide the size of the sample (n), we will assume it refers to the recorded 63 days as the sample size. We can use the formula for the confidence interval for a normally distributed population:
CI = μ ± Z*(σ/√n)
Where μ is the sample mean, Z is the z-score corresponding to the desired confidence level (for 99%, the z-score is approximately 2.576 according to the z-table), σ is the sample standard deviation, and n is the sample size.
Let's plug in the values:
Sample mean (μ) = 67.3
Z-score for 99% confidence level = 2.576
Sample standard deviation (σ) = 7.1
Sample size (n) = 63
The calculation of the confidence interval is as follows:
CI = 67.3 ± 2.576*(7.1/√63)
Calculate the margin of error (ME):
ME = 2.576 * (7.1/√63) = 2.576 * 0.8944 ≈ 2.3039
Now, calculate the confidence interval:
Lower limit = 67.3 - 2.3039 = 64.9961
Upper limit = 67.3 + 2.3039 = 69.6039
Therefore, the 99% confidence interval for the number of customers is approximately (65, 70).