Data from the Centers for Disease Control and Prevention indicate that weights of American adults in 2005 had a mean of 167 pounds and a standard deviation of 35 pounds.
-On October 5, 2005, a tour boat named the Ethan Allen capsized on Lake George in New York with 47 passengers aboard. In the inquiries that followed, it was suggested that the tour operators should have realized that the combined weight of so many passengers was likely to exceed the weight capacity of the boat, 7500 lbs. Based on this information, how surprising is it for a sample of 47 passengers to have an average weight of at least 7500/47 = 159.57 lbs?
A) Not surprising at all - the probability is over 90%.
B) Not surprising - the probability is between 50% and 60%.
C) Somewhat surprising - the probability is between 20% and 30%.
D) Very surprising - the probability is less than 5%.

Question

Quizplus · Accepted Answer

The probability of a sample of 47 passengers having an average weight of at least 159.57 lbs is over 90%. This is because the mean weight of American adults is 167 pounds and the standard deviation is 35 pounds. Therefore, the probability of a sample of 47 passengers having an average weight of at least 159.57 lbs is:P(X >= 159.57) = 1 - P(X < 159.57) = 1 - 0.0904 = 0.9096

Data from the Centers for Disease Control and Prevention Indicate