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Chapter 6: Q. 107 (page 431)

Cranky mower To start her old lawn mower, Rita has to pull a cord and hope for some luck. On any particular pull, the mower has a 20%chance of starting.

a. Find the probability that it takes her exactly 3 pulls to start the mower.

b. Find the probability that it takes her more than 6 pulls to start the mower.

Short Answer

Expert verified

(a)Thus, the required probability is 0.128

(b)Thus, the required probability is 0.24

Step by step solution

01

Part (a) Step 1: Given Information

Probability of success (p)=20%=0.20

Formula used:

The formula to compute the geometric distribution is:

P(X=x)=(1-p)x-1p

02

Part (a) Step 2: Simplificaiton

Consider, X be the random variable that follows the geometric distribution.

P(X=3)=(1-0.20){3-1}(0.20)=0.128

Thus, the required probability is 0.128.

03

Part (b) Step 1: Given information

Probability of success(p)=20percent

04

Part (b)  Step 2: Calculation

The probability that it will take more than 6 pulls can be calculated as:

P(X>6)=1-P(X鈮�6)=1-[P(X=1)+P(X=2)+鈥�.+P(X=6)]=1-[0.22+0.17+0.13+0.10+0.08+0.06]=0.24

Thus, the required probability is 0.24

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Most popular questions from this chapter

Skee Ball Refer to Exercise 4. Find the mean of X. Interpret this value.

Skee BallAna is a dedicated Skee Ball player (see photo in Exercise 4) who always rolls for the 50-point slot. The probability distribution of Ana鈥檚 score Xon a randomly selected roll of the ball is shown here. From Exercise 8, 渭X=23.8.

(a) Find the median of X.

(b) Compare the mean and median. Explain why this relationship makes sense based on the probability distribution.

Geometric or not? Determine whether each of the following scenarios describes a geometric setting. If so, define an appropriate geometric random variable.

a. Shuffle a standard deck of playing cards well. Then turn over one card at a time from the top of the deck until you get an ace.

b. Billy likes to play cornhole in his free time. On any toss, he has about a 20%chance of getting a bag into the hole. As a challenge one day, Billy decides to keep tossing bags until he gets one in the hole.

If Jeff gets 4 game pieces, what is the probability that he wins exactly 1 prize?

a. 0.25

b. 1.00

c. (41)(0.25)3(0.75)341(0.25)3(0.75)3

d. (41)(0.25)1(0.75)341(0.25)1(0.75)3

e.(0.75)3(0.75)1

Large Counts condition To use a Normal distribution to approximate binomial probabilities, why do we require that both npand n(1-p) be a t least 10?
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