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Chapter 5: Q 5.150. (page 242)

Under what three conditions are repeated trials of an experiment called Bernoulli trials?

Short Answer

Expert verified
  1. Two possible outcomes of the experiment.
  2. The trials are independent.
  3. Success probability remains constant from trial to trial.

Step by step solution

01

Step 1. Given information.

The given statement is:

Under what three conditions are repeated trials of an experiment called Bernoulli trials?

02

Step 2. The three conditions under which repeated trials of an experiment are called Bernoulli trials.

If the following three requirements are met, repeated trials of an experiment are known as Bernoulli trials:

1. There are two possible outcomes in the experiment, designated generally as "s" for success and "f" for failure.

2. The trials are independent, which means that the results of one experiment have no bearing on the results of the others.

3. The chance of success, known as the success probability and denoted by the letter p, remains constant from trial to trial.

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Most popular questions from this chapter

Fill in the blanks.

a.A relative-frequency distribution is to a variable as a ___ distribution is to a random variable.

b. A relative-frequency histogram is to a variable as a ___ histogram is to a random variable.

The Geometric Distribution. In this exercise, we discuss the geometric distribution, the probability distribution for the number of trials until the first success in Bernoulli trials. The geometric probability formula is

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

where Xdenotes the number of trials until the first success and pthe success probability. Using the geometric probability formula and Definition 5.9 on page 227. we can show that the mean of the random variable Xis 1/p.

To illustrate, consider the Mega Millions lottery, a multi-state jackpot draw game with a jackpot starting at $15 million and growing until someone wins. In order to play, the player selects five white numbers from the numbers 1-75 and one Mega Ball number from the numbers 1-15. Suppose that you buy one Mega Millions ticket per week. Let Xdenote the number of weeks until you win a prize.

(a) Find and interpret the probability formula for the random variable X. (Note: The probability of winning a prize with a single ticket is 0.0680.)

(b) Compute the probability that the number of weeks until you win a prize is exactly 3; at most 3: at least 3.

(c) On average, how long will it be until you win a prize?

Vitamin C and Aspirin A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains Bayer pills with 325 mg of aspirin. When testing claims about the mean contents of the pills, which would have more serious implications: rejection of the Spring Valley vitamin C claim or rejection of the Bayer aspirin claim? Is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of aspirin?

Suppose that A and B are events such that P(A)=14,P(B)=13and P(AorB)=12

Part (a). Are event A and B mutually exclusive ? Explain your answer.

Part (b) FindP(A&B)

Love Stinks? J. Fetto, in the article "Love Stinks" (American Demographics, Vol. 25. No. 1. pp. 10-11), reports that Americans split with their significant other for many reasons-including indiscretion, infidelity, and simply "growing apart." According to the article, 35% of American adults have experienced a breakup at least once during the last 10 years. Of nine randomly selected American adults, find the probability that the number, X, who have experienced a breakup at least once during the last 10 years is

(a) exactly five; at most five; at least five.

(b) at least one; at most one.

(c) between six and eight, inclusive.

(d) Determine the probability distribution of the random variable X.

(e) Strictly speaking, why is the probability distribution that you obtained in part (d) only approximately correct? What is the exact distribution called?
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