The lengths of text messages are normally distributed with a population standard deviation of 3 characters and an unknown population mean. If a random sample of 24 text messages i taken and results in a sample mean of 27 characters, find a 99% confidence interval for the population mean. Zo. 10Z0.0520.025 Zo. 01 Z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above. Select the correct answer below: a. (26.21,27.79) b. (25.99.28.01) c. (25.93,28.07)

Question

Everett

Mathematics

22 August, 01:00

The lengths of text messages are normally distributed with a population standard deviation of 3 characters and an unknown population mean. If a random sample of 24 text messages i taken and results in a sample mean of 27 characters, find a 99% confidence interval for the population mean. Zo. 10Z0.0520.025 Zo. 01 Z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above. Select the correct answer below: a. (26.21,27.79) b. (25.99.28.01) c. (25.93,28.07)

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Answers (1)

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Patrick Howard · Answer 1

25.4, 28.6

Step-by-step explanation:

Given parameters

sample size, n = 24

sample mean, X = 27

population standard deviation, s = 3

critical value, Zα/2, where α = 0.01

99% confidence Interval, CI, is given as follows

CI = X ± Zα/2 * (s/√n)

Zα/2 = Z0.01/2 = Z0.005 = 2.576

CI = 27 ± 2.576 * (3/√24)

= (25.42,28.57)