The label on 1-gallon cans of paint states that the amount of paint in the can is sufficient to paint 400 square feet. However, this number is quite variable. In fact, the amount of coverage is known to be \approx imately normally distributed with a standar

To find the sample size needed to estimate the true mean coverage of all 1-gallon cans to within 5 square feet with 95% confidence, we can use the formula: n = (z*?/E)^2 where: - n is the sample size - z is the z-score associated with the level of confidence (in this case, 1.96 for 95% confidence) - ? is the standard deviation of the coverage amount (25 square feet) - E is the maximum error of estimate we want (5 square feet) Plugging in the values, we get: n = (1.96*25/5)^2 n = 96.04 Rounding up to the nearest whole number, we get a sample size of 97. Therefore, a sample size of 97 cans of paint should be taken to estimate the true mean coverage of all 1-gallon cans to within 5 square feet with 95% confidence.