Question

1a. A new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 94% of all batteries have acceptable voltages. Let Y denote the number of batteries that must be tested.

(a) What is p(2), that is P(Y = 2)? (Round your answer to four decimal places.)

p(2) =   

(b) What is p(3)? [Hint: There are two different outcomes that result in Y = 3.]. (Round your answer to three decimal places.)

p(3) =   

(c) To have Y = 5, what must be true of the fifth battery selected?

The fifth battery must be an A.

The fifth battery must be a U.

List the four outcomes for which Y = 5. (Enter your answer in set notation.)

  

Determine p(5). (Round your answer to five decimal places.)

p(5) =   

(d) Use the pattern in your answers for parts (a)–(c) to obtain a general formula for p(y).

2b. A branch of a certain bank has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows:

F(x) =

0 x < 0

0.07 0 ≤ x < 1

0.17 1 ≤ x < 2

0.43 2 ≤ x < 3

0.62 3 ≤ x < 4

0.82 4 ≤ x < 5

0.99 5 ≤ x < 6

1 6 ≤ x

Calculate the following probabilities directly from the cdf:

(a) p(2), that is,

P(X = 2)

  

(b) P(X > 3)

  

(c)

P(2 ≤ X ≤ 5)

  

(d)

P(2 < X < 5)

Answer 1