A boat capsized and sank in a lake. Based on an assumption of a mean weight of 1

Question

A boat capsized and sank in a lake. Based on an assumption of a mean weight of 146?lb, the boat was rated to carry 50 passengers? (so the load limit was 7,300? lb). After the boat? sank, the assumed mean weight for similar boats was changed from146lb to 174lb. Complete parts a and b below.

a. Assume that a similar boat is loaded with 50 ?passengers, and assume that the weights of people are normally distributed with a mean of 179.9lb and a standard deviation of 39.9 lb. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 146 lb. The probability is ____. (Round to four decimal places as? needed.)

b. The boat was later rated to carry only 13 ?passengers, and the load limit was changed to 2,262 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 174 ?(so that their total weight is greater than the maximum capacity of 2,262lb). The probability is ____.?(Round to four decimal places as? needed.)

Do the new ratings appear to be safe when the boat is loaded with 13 ?passengers? Choose the correct answer below.

A. Because the probability of overloading is lower with the new ratings than with the old? ratings, the new ratings appear to be safe.

B.Because there is a high probability of? overloading, the new ratings do not appear to be safe when the boat is loaded with 13 passengers.

C. Because 179.9 is greater than 174?, the new ratings do not appear to be safe when the boat is loaded with 13 passengers.

D.Because there is a high probability of? overloading, the new ratings appear to be safe when the boat is loaded with 13 passengers.

Explanation / Answer

1) Z = (146-179.9)/(39.9/sqrt(50))= -6.007

P(z>-6.007) = 0.9999 from p-value table

2) Z = (174-179.9)/(39.9/sqrt(13)) = -0.5333

P(z>-1.0455) = 0.7019 from p-value table

3)

A. Because the probability of overloading is lower with the new ratings than with the old? ratings, the new ratings appear to be safe.

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