Answer:
(a) The mean is 4.31 pounds. The variance is 51.42 pounds.
(b) The average shipping cost of a package is $10.78.
(c) The probability that the weight of a package exceeds 59 pounds is 0.0027.
Step-by-step explanation:
The probability density function of the weight of packages is:
(a)
The formula for expected value (or mean) of <em>X</em> is:
Compute the expected value of <em>X</em> as follows:
Thus, the mean is 4.31 pounds.
The formula to compute the variance is:
Compute the E (<em>X²</em>) as follows:
The variance is:
Thus, the variance is 51.42 pounds.
(b)
It is provided that the shipping cost for per pound is, C = $2.50.
Compute the average shipping cost of a package as follows:
Thus, the average shipping cost of a package is $10.78.
(c)
Compute the probability that the weight of a package exceeds 59 pounds as follows:
Thus, the probability that the weight of a package exceeds 59 pounds is 0.0027.