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Chapter 5: Q1 (page 220)
Is a probability distribution defined if the only possible values of a random variable are 0, 1,2, 3, and P(0) = P(1) = P(2) = P(3) = 1/3?
No, the probability distribution is not defined if the only possible values of a random variable are 0, 1,2, 3, and .
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In Exercises 9–16, use the Poisson distribution to find the indicated probabilities.
Births In a recent year, NYU-Langone Medical Center had 4221 births. Find the mean number of births per day, then use that result to find the probability that in a day, there are 15 births. Does it appear likely that on any given day, there will be exactly 15 births?
In Exercises 7–14, determine whether a probability
distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
A sociologist randomly selects single adults for different groups of three, and the random variable xis the number in the group who say that the most fun way to flirt is in person(based on a Microsoft Instant Messaging survey).
x | P(x) |
0 | 0.091 |
1 | 0.334 |
2 | 0.408 |
3 | 0.166 |
Ultimate Binomial Exercises! Exercises 37–40 involve finding binomial probabilities, finding parameters, and determining whether values are significantly high or low by using the range rule of thumb and probabilities.
Hybrids 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. 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 152 yellow peas either significantly low or significantly high?
b. Find the probability of exactly 152 yellow peas.
c. Find the probability of 152 or more yellow peas.
d. Which probability is relevant for determining whether 152 peas is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 152 yellow peas significantly high?
e. What do the results suggest about Mendel’s claim of 25%?
Groups of people aged 15–65 are randomly selected and arranged in groups of six. The random variable xis the number in the group who say that their family and / or partner contribute most to their happiness (based on a Coca-Cola survey). The accompanying table lists
the values of xalong with their corresponding probabilities. Does the table describe a probability distribution? If so, find the mean and standard deviation.
x | P(x) |
0 | 0+ |
1 | 0.003 |
2 | 0.025 |
3 | 0.111 |
4 | 0.279 |
5 | 0.373 |
6 | 0.208 |
In Exercises 6–10, use the following: Five American Airlines flights are randomly selected, and the table in the margin lists the probabilities for the number that arrive on time (based on data from the Department of Transportation). Assume that five flights are randomly selected.
What is the probability that fewer than three of the five flights arrive on time?
x | P(x) |
0 | 0+ |
1 | 0.006 |
2 | 0.051 |
3 | 0.205 |
4 | 0.409 |
5 | 0.328 |
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