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Chapter 6: Problem 60

A coin will be flipped four times, and the number of heads recorded. Explain why this is a binomial experiment. Check all four required conditions.

Short Answer

Expert verified
Yes, flipping a coin four times and recording the number of heads is a binomial experiment because it satisfies all four conditions of a binomial experiment: it consists of a sequence of identical trials, each trial has two possible outcomes, the probability of success is constant for each trial, and the trials are independent.

Step by step solution

01

Check first condition

The first condition states the process must consist of a sequence of n identical trials. Here, flipping a coin four times corresponds to four identical trials. Thus, the first condition is satisfied.
02

Check second condition

The second condition states that only two outcomes are possible on each trial. Here, these are Heads (H) and Tails (T) on each coin flip. Therefore, the second condition is met.
03

Check third condition

The third condition states that the probability of success does not change from trial to trial. In this case, the probability of flipping a head (p), which is 0.5, remains the same for each flip. Thus, the third condition is satisfied.
04

Check fourth condition

The fourth condition is that the trials should be independent; the outcome on one trial does not affect the outcome on other trials. In this case, the outcome of a coin toss does not affect the outcomes of the other coin tosses. Hence, the fourth condition is also met.

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Most popular questions from this chapter

The Normal model \(N(150,10)\) describes the distribution of scores on the LSAT, a standardized test required by most law schools. Which of the following questions asks for a probability, and which asks for a measurement? Identify the type of problem and then answer the given question. a. A law school applicant scored at the 60 th percentile on the LSAT. What was the applicant's LSAT score? b. A law school applicant scored 164 on the LSAT. This applicant scored higher than what percentage of LSAT test takers?

In Toronto, Canada, \(55 \%\) of people pass the drivers' road test. Suppose that every day, 100 people independently take the test. a. What is the number of people who are expected to pass? b. What is the standard deviation for the number expected to pass? c. After a great many days, according to the Empirical Rule, on about \(95 \%\) of these days, the number of people passing will be as low as ________ and as high as ________. (Hint: Find two standard deviations below and two standard deviations above the mean.)

Use the table or technology to find the answer to each question. Include an appropriately labeled sketch of the Normal curve for each part. Shade the appropriate region. A section of the Normal table is provided in the previous exercise. a. Find the area to the left of a \(z\) -score of \(0.92\). b. Find the area to the right of a z-score of \(0.92\).

Alaska Airlines has an on-time arrival rate of \(88 \%\). Assume that in one day, this airline has 1200 flights. Suppose we pick one day in December and find the number of ontime Alaska Airline arrivals. Why would it be inappropriate to use the binomial model to find the probability that at least 1100 of the 1200 flights arrive on time? What condition or conditions for use of the binomial model is or are not met?

The average birth weight of domestic cats is about 3 ounces. Assume that the distribution of birth weights is Normal with a standard deviation of \(0.4\) ounce. a. Find the birth weight of cats at the 90 th percentile. b. Find the birth weight of cats at the 10 th percentile.
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