교과서 질문
Using Probabilities for Significant Events
a. Find the probability of getting exactly 1 match.
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Ch. 5 - Discrete Probability Distributions
Triola14th EditionElementary StatisticsISBN: 9780137366446
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Table of contents
- Ch. 1 - Introduction to Statistics88
- Ch. 2 - Exploring Data with Tables and Graphs70
- Ch. 3 - Describing, Exploring, and Comparing Data66
- Ch. 4 - Probability112
- Ch. 5 - Discrete Probability Distributions109
- Ch. 6 - Normal Probability Distributions122
- Ch. 7 - Estimating Parameters and Determining Sample Sizes107
- Ch. 8 - Hypothesis Testing75
- Ch. 9 - Inferences from Two Samples94
- Ch. 10 - Correlation and Regression80
- Ch. 11 - Goodness-of-Fit and Contingency Tables29
- Ch. 12 - Analysis of Variance42
5장, 문제 5.2.32a
In Exercises 31 and 32, assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods (as in one of Mendel’s famous experiments).
Hybrids Assume that offspring peas are randomly selected in groups of 16.
a. Find the mean and standard deviation for the numbers of peas with green pods in the groups of 16.
검증된 단계별 안내1
Step 1: Recognize that this is a binomial distribution problem because there are two possible outcomes for each pea: having green pods (success) or not having green pods (failure). The probability of success (green pods) is given as p = 0.75, and the number of trials (n) is 16.
Step 2: Recall the formula for the mean (μ) of a binomial distribution: μ = n × p. Substitute the given values of n = 16 and p = 0.75 into this formula to calculate the mean.
Step 3: Recall the formula for the standard deviation (σ) of a binomial distribution: σ = √(n × p × (1 - p)). Substitute the given values of n = 16, p = 0.75, and (1 - p) = 0.25 into this formula to calculate the standard deviation.
Step 4: Simplify the expressions for both the mean and the standard deviation. For the mean, multiply n and p. For the standard deviation, calculate the product n × p × (1 - p) and then take the square root of the result.
Step 5: Interpret the results. The mean represents the expected number of peas with green pods in a group of 16, and the standard deviation measures the variability in the number of peas with green pods across different groups of 16.
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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 case, the success is defined as a pea having green pods, with a probability of 0.75. The distribution is characterized by two parameters: the number of trials (n) and the probability of success (p).
추천 영상:
가이드 코스
03:28
Mean & Standard Deviation of Binomial Distribution
Mean of a Binomial Distribution
The mean of a binomial distribution can be calculated using the formula μ = n * p, where n is the number of trials and p is the probability of success. For this problem, with 16 peas and a probability of 0.75 for green pods, the mean number of peas with green pods can be determined by substituting these values into the formula.
추천 영상:
가이드 코스
03:28Mean & Standard Deviation of Binomial Distribution
Standard Deviation of a Binomial Distribution
The standard deviation of a binomial distribution is calculated using the formula σ = √(n * p * (1 - p)). This formula accounts for the variability in the number of successes across the trials. In this scenario, it helps quantify how much the number of peas with green pods is expected to deviate from the mean in groups of 16.
추천 영상:
가이드 코스
03:28Mean & Standard Deviation of Binomial Distribution
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교과서 질문
Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).
Using Probabilities for Significant Events
a. Find the probability of getting exactly 2 matches.
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교과서 질문
In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 5.5 per year, as in Example 1; and proceed to find the indicated probability.
Hurricanes
a. Find the probability that in a year, there will be 7 hurricanes.
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교과서 질문
Politics The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning the order in which candidates’ names appeared on voting ballots. Among 41 different ballots, Democrats were assigned the desirable first line 40 times. Assume that Democrats and Republicans are assigned the first line using a method of random selection so that they are equally likely to get that first line.
a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the result of 40 first lines for Democrats significantly high?
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교과서 질문
Expected Value in North Carolina’s Pick 4 Game In North Carolina’s Pick 4 lottery game, you can pay \(1 to select a four-digit number from 0000 through 9999. If you select the same sequence of four digits that are drawn, you win and collect \)5000.
a. How many different selections are possible?
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교과서 질문
One of Mendel’s famous experiments with peas resulted in 580 offspring, and 152 of them were yellow peas. Mendel claimed that under the same conditions, 25% of offspring peas would be yellow. Assume that Mendel’s claim of 25% is true, and assume that a sample consists of 580 offspring peas.
b. Find the probability of exactly 152 yellow peas.
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