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 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.

Answer 1

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