Question

Suppose that the weight of a package in a package delivery service is right-skewed with mean 1 pound and standard deviation 0.5774 pounds. Its density curve is shown in the following graph.

(a) If you randomly choose 64 packages, find the sampling distribution of their average weight. Please indicate the shape, mean and standard deviation.

(b) For randomly selected 64 packages, find the probability that their average weight is above 1.02 pounds. Let X¯ be the average weight of randomly selected 64 packages.

Answer 1

Solution :

Given that ,

mean = = 1

standard deviation = = 0.5774

a)

n = 64

= = 1 and

= / n = 0.5774 / 64 = 0.07218

b)

P( > 1.02) = 1 - P( < 1.02)

= 1 - P(( - ) / < (1.02 - 1) / 0.07218)

= 1 - P(z < 0.28)

= 1 - 0.6103 Using standard normal table.

= 0.3897

Probability = 0.3897