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Back to 7.3 Using the Central Limit Theorem

7.3 Exercise 14

Avg difficulty 2.5

Use the following information to answer the next ten exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

  1. What is the distribution for the weights of one 25-pound lifting weight? What is the mean and standard deivation?
  2. What is the distribution for the mean weight of 100 25-pound lifting weights?
  3. Find the probability that the mean actual weight for the 100 weights is less than 24.9.

OpenStax Introductory Statistics 2e, 7.3 Using the Central Limit Theorem, exercise 14

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Adapted from Introductory Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Statistics 2e. Imported at revision 50ec917.