please show work. 2.) A ski gondola in Vail, Colorado that carries skiers up a mountain bears a plaque stating thatthe maximum capacity is 12 people or 2004 lb. A worst-case scenario would be 12 adult malepassengers, since they tend to be heavier than women or children. Assume adult male weightsare normally distributed with a mean of 188.6 Ib. and standard deviation of 38.9 lb.

n=12, maximum weight = 2004 mean = 188.6 std.dev = 38.9 average weight limit for gondola = 2004/12 = 167 so capacity will be exceeded if 12 people have mean weight greater than 167 lbs. so we will find the probability that 12 randomly selected passenger have mean greater than 167 lbs and if this probability is less than 0.05, then it is good to conclude that gondola is in correct weight limit otherwise not. For 12 passengers: sample mean = 167 population mean = 188.6 standard deviation = 38.9 standard error = 38.9/12 = 11.23 P(x¯ >167) = 0.9728 Since, for a group of 12 passenger, the probability of having mean weight greater than 167 lbs is very high. Hence, gondola does not have correct weight limit, so it is recommended that no. of allowed passengers should be reduced. gondola does not have correct weight limit, because there is a high probability that the gondola will be overloaded if it is occupied by 12 passengers