Answer :
Final answer:
To find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 139 lb, we need to calculate the z-score for the given mean weight of 139 lb. The probability is 0.0000.
Explanation:
To find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 139 lb, we need to calculate the z-score for the given mean weight of 139 lb.
Z = (mean - population mean) / (standard deviation / sqrt(sample size))
Z = (139 - 182.4) / (40.3 / sqrt(50))
After finding the z-score, we can then find the probability using a z-table or a calculator. The probability is the area under the normal curve to the right of the z-score.
The probability that the boat is overloaded is 0.0000, rounded to four decimal places.
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