Question

1. (1) A company that produces fine crystal knows from experience that 10% of its goblets have cosmetic flaws and must be classified as “seconds.”

   (a) If 6 goblets are randomly selected, what is the probability that only one is considered a second? (b) If 6 goblets are randomly selected, what is the probability that at least 2 are seconds?

   (c) Find EX, V X, and SDX

2. (2) A coffee shop serves an average of 75 customers per hour during the morning rush.

   (a) What is the probability that the shop serves exactly 70 customers during the morning rush hour?

   (b) What is the probability that the shop serves only 60 customers? (c) Find EX, V X, and SDX

3. (3) Suppose the force acting upon a column that helps to support a building is normally distributed with mean 15.0 kips and standard deviation 1.25 kips (i.e. X ∼ N (μ, σ) = X ∼ N (15, 1.25)). Calculate the following:

   (a) P(X≤15)(b) P(X≤17)(c) P(X≥10)

   (d) P(14<X<18)
   (e) Find the value of the force (in kips) that the highest 7% of forces on the column are

Answer 1