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Confidence Interval; Sampling Distribution; Mean and Standard Deviation

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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.

Please see the attachment for correct formatting and complete information.

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Solution Summary

The solution gives step-by-step equational answers to each question, provided in an attachment.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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