Question

QUESTION 2: Historically, 78.28% of packages delivered by UPS are on time. Suppose 136 deliveries are randomly selected for quality control. What is the probability that less than 75.56% of the deliveries were on time?

QUESTION 3: You are working as a quality control manager for FedEx and are responsible for delivery time customer satisfaction. Historically, the worldwide average delivery time is 17.2 days with a standard deviation of 6.412 days. You select 57 random deliveries over the course of a few months. Given your historical parameters still hold true, what is the probability that the average time until delivery is between 16.26 and 16.74 days?

QUESTION 4: Fill in the blank. Suppose that NBA players average 24.03 points per game with a standard deviation of 8.673. A random sample of 31 players is taken. There is a 47% chance that the average points per game is greater than ________ points.

Answer 1

2) = p = 0.7828

    = sqrt(p(1 - p)/n)

          = sqrt(0.7828 * (1 - 0.7828)/136)

          = 0.0354

P( < 0.7556)

= P(( - )/ < (0.7556 - )/)

= P(Z < (0.7556 - 0.7828)/0.0354)

= P(Z < -0.77)

= 0.2206

3) P(16.26 < < 16.74)

= P((16.26 - )/() < ( - )/() < (16.74 - )/())

= P((16.26 - 17.2)/(6.412/) < Z < (16.74 - 17.2)/(6.412/))

= P(-1.11 < Z < -0.54)

= P(Z < -0.54) - P(Z < -1.11)

= 0.2946 - 0.1335

= 0.1611

4) P( > x) = 0.47

or, P(( - )/() > (x - )/()) = 0.47

or, P(Z > (x - 24.03)/(8.673/)) = 0.47

or, P(Z < (x - 24.03)/(8.673/)) = 0.53

or, (x - 24.03)/(8.673/) = 0.08

or, x = 0.08 * (8.673/) + 24.03

or, x = 24.155