Confidence Interval; Sampling Distribution; Mean and Standard Deviation

1. A parcel service randomly selected 48 packages it received. The sample has a mean weight of 18.6 pounds. Assume that σ = 3.4 pounds. Construct a 90% confidence interval for the true mean weight, μ, of all packages received by the parcel service.

2. A phone company wants to estimate the mean duration of local calls. Assume σ = 3.0. the sample size is 540. Find the margin of error in estimating μ at the 90% level of confidence.

3. The mean and standard deviation for a population are 107 and 14, respectively. Samples of size 49 are selected randomly from the population. Find the mean and standard deviation of the sampling distribution.

4. The weekly earnings of students in one age group are approximately normally distributed with a standard deviation of 36 dollars. A researcher wishes to estimate the mean weekly earnings. Find the sample size needed if she requires a 90% degree of confidence that the sample mean will not differ from the population by more than 3 dollars.

5. A sample of cereal boxes were selected, and their weights in ounces were recorded in the attachment. Determine a 95% confidence interval for the mean weight of cereal in all boxes.

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