Question

The United States Coast Guard assumes the mean weight of passengers in commercial boats is 185 pounds. The previous value was lower, but was raised after a tragic boating accident. The standard deviation of passenger weights is 26.7 pounds. The weights of a random sample of 48 commercial boat passengers were recorded. The sample mean was determined to be 177.6 pounds. Find the probability that a random sample of passengers will have a weight that is as extreme or more extreme (either above or below the mean) than was observed in this sample. (Round your answer to 3 decimal places. Example: If the answer is 0.8976 then you would enter 0.898 in the answer box.) Note: As extreme or more extreme means that we are not only interested in values that are lower than the ones we observed, but also values that are as far away from the mean as ours in the positive direction.

Answer 1

0.973

Explanation:

Given the following :

Population mean (μ) = 185

Standard deviation (σ) = 26.7

Sample mean (m) = 177.6

Sample size (n) = 48

P(m > 177.6)

Z = (m - μ) / σ/√n

Z = (177.6 - 185) / (26.7/√48)

Z = −1.920176

P( z > - 1.920) = 1 - p(z < - 1.92)

Using the z table :

1 - p(z < - 1.920) = 1 - 0.0274 = 0.9726

= 0.973