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 70 passengers (so the load limit was 10,220 lb). After the boat sank, the assumed mean weight for similar boats was changed from 146 lb to 170 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 174.6 lb and a standard deviation of 39.9 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 146 lb.
Solution :
Given that ,
_{} = 174.6
_{} = / n = 39.9 / 70 = 4.77
P( > 146 ) = 1 - P( < 146 )
= 1 - P[( - _{} ) / _{} < (146 - 174.6) / 4.77 ]
= 1 - P(z < -6.0)
= 1 - 0
= 1
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