Question

The weight of a single bag checked by an airplane passenger follows a distribution that is right skewed with a mean of 38 pounds and a standard deviation of 6.2 pounds. If a random sample of 96 bags is selected, what is the probability that the average weight of the bags exceeds 40 pounds?

Answer 1

0.0008

Explanation:

P(z>3.16) = 0.0008.

Answer 2

0.0007872

Explanation:

-Since the sample size is large enough, we apply the normal distribution to find the probability.

#Given n=96, mean=38 and standard deviation=6.2 pounds, the probability can be calculated as:

`P(X>40)=P(z>(X-\mu)/(\sigma/√(n)))\\\\=P(z>(40-38)/(6.2/√(96)))\\\\=P(z>3.1606}\\\\=0.0007872`

Hence, the probability is 0.0007872