![]() ![]() Therefore, the shop foreman needs to select a sample of at least 57 cars to estimate the average time it takes to replace a fuel pump with 91% confidence that the true average time is within 12 minutes of the sample average. Since we can't have a fractional sample size, we round up to the nearest whole number: Sample size = (z * standard deviation / margin of error)^2 We can rearrange this formula to solve for the sample size: Where z is the z-score for the desired level of confidence (in this case, 1.645 for 91% confidence). Margin of error = z * (standard deviation / sqrt(sample size)) To solve this problem, we can use the formula for the margin of error: We need to determine the sample size required to achieve this level of confidence. We assume the standard deviation of all times is 25 minutes.Ĥ. We want to be 91% confident that the true average time is within 12 minutes of the sample average.ģ. Being shop foreman, you'll be the leader of your mechanic staff in a workshop or a plant, and responsible for overseeing and managing the daily operations as well as the staff members who manufacture products, make services, or repairs. We need to estimate the average time it takes to replace a fuel pump in a car.Ģ. ![]()
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