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In: Statistics and Probability

The standard deviation of the population of airline departure delays is σ = 23 minutes. Suppose...

The standard deviation of the population of airline departure delays is σ = 23 minutes. Suppose that we choose an SRS of 152 departures. Calculate the standard deviation of their mean length in minutes. Then apply the Central Limit Theorem and the 68-95-99.7 Rule to complete the following statement: “about 95% of all samples will have its mean within ± ________ minutes of the true population mean μ.”

Round your answer to 2 decimal places of accuracy.

Solutions

Expert Solution

Solution :

Given that

standard deviation = = 23

n = 152

= / n = 23 / 152 = 1.87

P( - 2 < <   + 2 ) = 95%

=   ± 2 = 95%

=    ± 2 * 1.87 = 95%

=   ± 3.74 = 95%

“about 95% of all samples will have its mean within  ± 3.74 minutes of the true population mean μ.”

orchestra answered 2 years ago
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