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Chapter 6: Q. 87 (page 428)

Take a spin Refer to Exercise 83. Calculate and interpret P(X≤7)

Short Answer

Expert verified

There are 7.26%chances that spinner would land in the blue region at most 7 times.

Step by step solution

01

Given Information

Number of trials (n)=12

Probability of success(p)=0.80

02

Simplification

Consider, Xbe the random variable that follows the binomial distribution with parameters n=12and p=0.80.

P(X≤7)can be calculated as:

P(X≤7)=P(X=0)+P(X=1)+….+P(X=7)=∑r=07Cr12×(0.80)r×(1-0.80)12-r=0.0726

Hence, the probability is0.0726

Interpretation:

There are 7.26%chances that spinner would land in the blue region at most 7 times.

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Most popular questions from this chapter

Take a spin An online spinner has two colored regions_blue and yellow. According to the website, the probability that the spinner lands in the blue region on any spin is 0.80. Assume for now that this claim is correct. Suppose we spin the spinner 12 times and let X=the number of times it lands in the blue region.

a. Explain why Xis a binomial random variable.

b. Find the probability that exactly 8 spins land in the blue region.

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

a. A popular brand of cereal puts a card bearing the image of 1 of 5 famous NASCAR drivers in each box. There is a 1/5chance that any particular driver's card ends up in any box of cereal. Buy boxes of the cereal until you have all 5 drivers' cards.

b. In a game of 4-Spot Keno, Lola picks 4 numbers from 1 to 80 . The casino randomly selects 20 winning numbers from 1 to 80 . Lola wins money if she picks 2 or more of the winning numbers. The probability that this happens is \(0.259\). Lola decides to keep playing games of 4-Spot Keno until she wins some money.

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

Spell-checking Spell-checking software catches “nonword errors,” which result in a string of letters that is not a word, as when “the” is typed as “teh.” When undergraduates are asked to write a 250-word essay (without spell-checking), the number Y of nonword errors in a randomly selected essay has the following probability distribution

Part (a). Write the event “one nonword error” in terms of Y. Then find its probability.

Part (b). What’s the probability that a randomly selected essay has at least two nonword errors?

Benford’s law and fraud

(a) Using the graph from Exercise 21, calculate the standard deviation σY. This gives us an idea of how much variation we’d expect in the employee’s expense records if he assumed that first digits from 1 to 9 were equally likely.

(b) The standard deviation of the first digits of randomly selected expense amounts that follow Benford’s law is σX=2.46. Would using standard deviations be a good way to detect fraud? Explain your answer.

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