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Ch. 4 - Discrete Probability Distributions
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Larson 8th EditionCh. 4 - Discrete Probability Distributions문제 4.RE.15a
4장, 문제 4.RE.15a

In Exercises 13–16, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B.
Seventy-two percent of U.S. civilian employees have access to medical care benefits. You randomly select nine civilian employees. Find the probability that the number who have access to medical care benefits is (a) exactly six

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Step 1: Recognize that this is a binomial probability problem. The binomial distribution is used when there are a fixed number of independent trials, each with two possible outcomes (success or failure). Here, the number of trials (n) is 9, the probability of success (p) is 0.72, and the number of successes (x) is 6.
Step 2: Write the formula for the binomial probability: P(X = x) = (n choose x) * p^x * (1 - p)^(n - x). Here, (n choose x) is the binomial coefficient, which can be calculated as n! / [x! * (n - x)!].
Step 3: Substitute the given values into the formula. For this problem, n = 9, x = 6, and p = 0.72. The formula becomes: P(X = 6) = (9 choose 6) * (0.72)^6 * (1 - 0.72)^(9 - 6).
Step 4: Calculate the binomial coefficient (9 choose 6). This is done using the formula: (9 choose 6) = 9! / [6! * (9 - 6)!]. Simplify this expression to find the value of the coefficient.
Step 5: Compute the probability by multiplying the binomial coefficient by (0.72)^6 and (1 - 0.72)^3. This will give you the probability that exactly 6 out of 9 employees have access to medical care benefits.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Binomial Distribution

The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. In this context, it applies to the scenario of selecting employees with a specific probability of having medical care benefits. The distribution is defined by two parameters: the number of trials (n) and the probability of success (p).
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가이드 코스
03:28
Mean & Standard Deviation of Binomial Distribution

Probability Mass Function (PMF)

The probability mass function for a binomial distribution gives the probability of obtaining exactly k successes in n trials. It is calculated using the formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where 'n choose k' represents the binomial coefficient. This function is essential for determining the likelihood of specific outcomes, such as exactly six employees having access to benefits.
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5:37
Introduction to Probability

Binomial Coefficient

The binomial coefficient, denoted as 'n choose k' or C(n, k), represents the number of ways to choose k successes from n trials. It is calculated using the formula C(n, k) = n! / (k!(n-k)!), where '!' denotes factorial. This concept is crucial for calculating probabilities in binomial distributions, as it quantifies the different combinations of successes and failures.
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가이드 코스
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Coefficient of Determination
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교과서 질문

The Centers for Disease Control and Prevention (CDC) is required by law to publish a report on assisted reproductive technology (ART). ART includes all fertility treatments in which both the egg and the sperm are used. These procedures generally involve removing eggs from a patient’s ovaries, combining them with sperm in the laboratory, and returning them to the patient’s body or giving them to another patient.

You are helping to prepare a CDC report on young ART patients and select at random 6 ART cycles of patients under 35 years of age for a special review. None of the cycles resulted in a live birth. Your manager feels it is impossible to select at random 10 ART cycles that do not result in a live birth. Use the pie chart at the right and your knowledge of statistics to determine whether your manager is correct.

a. How would you determine whether your manager is correct, that it is impossible to select at random six ART cycles that do not result in a live birth?

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교과서 질문

In Exercises 13–16, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B.

Seventy-two percent of U.S. civilian employees have access to medical care benefits. You randomly select nine civilian employees. Find the probability that the number who have access to medical care benefits is (b) at least six

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교과서 질문

In Exercises 13–16, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B.

Fifty-three percent of U.S. adults support attempting to land an astronaut on Mars. You randomly select eight U.S. adults. Find the probability that the number who support attempting to land an astronaut on Mars is (b) at least three

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교과서 질문

In Exercises 13–16, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B.

Seventy-two percent of U.S. civilian employees have access to medical care benefits. You randomly select nine civilian employees. Find the probability that the number who have access to medical care benefits is (c) more than six.

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교과서 질문

In Exercises 13–16, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B.

Fifty-three percent of U.S. adults support attempting to land an astronaut on Mars. You randomly select eight U.S. adults. Find the probability that the number who support attempting to land an astronaut on Mars is (a) exactly three

128
views
교과서 질문

In Exercises 13–16, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B.

Fifty-three percent of U.S. adults support attempting to land an astronaut on Mars. You randomly select eight U.S. adults. Find the probability that the number who support attempting to land an astronaut on Mars is (c) more than three.

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