Question

I need help on question 13 for a b and c

Answer 1

b) We have to calculate the probability that a group of 25 men exceeds the average allowed weight per passenger.

As the water taxi has a load limit of 3500 lb, the maximum average weight per passenger is 3500/25 = 140 lb.

Then, we can calculate the probability that the mean of a sample of size n = 25 is greater than 140 lb.

The population distribution from where the sample is taken has a mean of 189 lb and a standard deviation of 39 lb.

We can calculate the z-score for M = 140 lb for this sample as:z

`z=(M-\mu)/(\sigma\/√(n))=(140-189)/(39\/√(25))=(-49)/(39\/5)\approx-6.28`

Then, the probabilitty can be expressed as:

`P(M>140)=P(Z>-6.28)\approx1`

It is almost certain that the sample mean will be greater than 140 lb.

c) We now have to calculate the probability that a sample of size n = 20 has a mean that is greater than 175 lb, the new load limit per passenger.

We can repeat the procedure calculating the z-score with this new values (M = 175 and n = 20):

`z=(M-\mu)/(\sigma\/√(n))=(175-189)/(39\/√(20))\approx(-14)/(8.721)\approx-1.6`

Then, we can look up the probability for the standard normal distribution when z = -1.6 and obtain:

We can express this as:

`P(M>175)=P(z>-1.6)=0.9452`

d) As the probabilty of exceeding the load limit per passenger is too high, we can consider that 20 passengers is still not safe enough.

Answer:

b) P(M > 140) = 1

c) P(M > 175) = 0.9452

d) Not safe