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Back to 7.3 Using the Central Limit Theorem

7.3 Exercise 11

Avg difficulty 2.5

A study was done regarding attendance at Broadway shows in New York City. The age range of the attendees was 14 to 61. The mean age was 30.9 years with a standard deviation of nine years.

  1. In a sample of 25 attendees, what is the probability that the mean age is less than 35?
  2. Is it likely that the mean age of the sample group could be more than 50 years? Interpret the results.
  3. In a sample of 49 attendees, what is the probability that the sum of the ages is no less than 1,600?
  4. Is it likely that the sum of the ages of the 49 attendees is at most 1,595? Interpret the results.
  5. Find the 95th percentile for the sample mean age of 65 attendees. Interpret the results.
  6. Find the 90th percentile for the sum of the ages of 65 attendees. Interpret the results.

OpenStax Introductory Statistics 2e, 7.3 Using the Central Limit Theorem, exercise 11

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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.