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Chapter 6: Q. 8. (page 367)

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

Short Answer

Expert verified

μ=23.8

Step by step solution

01

Step 1. Given information.

Score1020304050
Probability0.320.270.190.150.07
02

Step 2. The mean of X. 

The expected value (or mean) is the sum of the product of each possibility r with its probability P(X= x):

μ=ΣxP(X=x)=10x0.32+20x0.27+30x0.19+40x0.15+50x0.07μ=23.8

On average, the score on a randomly selected roll of the ball is 23.8.

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Most popular questions from this chapter

Taking the train Refer to Exercise 80 . Use the binomial probability formula to find P(Y=4). Interpret this value.

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p ?

a. n=10,p=0.5

b. n=40,p=0.88

c. n=100,p=0.2

d. n=100,p=0.99

e.n=1000,p=0.003

Bag check Refer to Exercise 91 .

a. Calculate and interpret the mean of R.

b. Calculate and interpret the standard deviation of R.

Using Benford's law According to Benford's law (Exercise 15, page 377), the probability that the first digit of the amount of a randomly chosen invoice is an 8 or a 9 is 0.097. Suppose you examine randomly selected invoices from a vendor until you find one whose amount begins with an 8 or a 9 .

a. How many invoices do you expect to examine before finding one that begins with an 8 or 9 ?

b. In fact, the first invoice you find with an amount that starts with an 8 or 9 is the 40 th invoice. Does this result provide convincing evidence that the invoice amounts are not genuine? Calculate an appropriate probability to support your answer.

Toothpaste Ken is traveling for his business. He has a new 0.85-ounce tube of toothpaste that’s supposed to last him the whole trip. The amount of toothpaste Ken squeezes out of the tube each time he brushes is independent, and can be modeled by a Normal distribution with mean 0.13 ounce and standard deviation 0.02 ounce. If Ken brushes his teeth six times on a randomly selected trip, what’s the probability that he’ll use all the toothpaste in the tube?
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