5.5-8 Transcription of the text for an educational website:---**5.5-7.** Suppose that the distribution of the weight of a prepackaged 1-pound bag is $N(1.01, 0.007^2)$. Selecting 3-pound bags of weights of prepackaged 1-pound bags, the distribution of errors is $N(3/2, 0.006^2)$. Find the probability that the sum of the prepackaged 1-pound bags exceeds the weight of one 3-pound bag. First, determine the distribution of $K$, the sum of three 1-pound bags, then compute $P(Y > W)$, where $Y$ is the weight of a 3-pound bag.**5.5-8.** Let $X$ denote the wing length in millimeters of a male gallinule and assume that $X\sim N(84.09, 39.37)$ and the wing length $Y$ of a female gallinule is $N(71.93, 50.88)$ and that $X$ and $Y$ are independent. If a male and female gallinule are captured, what is the probability that $X$ is greater than $Y$?**5.5-9.** Suppose that the length of life in hours (say, $X$) of a light bulb manufactured by company $A$ is $N(800, 14400)$ and the length of life in hours (say, $Y$) of a light bulb manufactured by company $B$ is $N(850, 22500)$. One bulb is randomly selected from each company and is burned until "dead." (a) Find the probability that the length of life of the bulb from company $A$ exceeds the length of life of the bulb from company $B$ by at least 15 hours. (b) Find the probability that at least one of the bulbs "lives" for at least 920 hours.**5.5-10.** A consumer buys $n$ light bulbs, each of which has a distribution that has a mean of 800 hours, a standard deviation of 100 hours, and a normal distribution. A light bulb is replaced by another as soon as it burns out. Assuming...(Note: The image cuts off at this

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Description: 5.5-8 Transcription of the text for an educational website:---**5.5-7.** Suppose that the distribution of the weight of a prepackaged 1-pound bag is $N(1.01, 0.007^2)$. Selecting 3-pound bags of weights of prepackaged 1-pound bags, the distribution

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Answered: 5.5-8. Let X denote the male gallinule…

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5.5-8. Let X denote the male gallinule and Y th female gallinule. Assum Y is N(171.93, 50.88) an If a male and a female probability that X is gre

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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5.5-8

Transcription of the text for an educational website:

---

**5.5-7.** Suppose that the distribution of the weight of a prepackaged 1-pound bag is $N(1.01, 0.007^2)$. Selecting 3-pound bags of weights of prepackaged 1-pound bags, the distribution of errors is $N(3/2, 0.006^2)$. Find the probability that the sum of the prepackaged 1-pound bags exceeds the weight of one 3-pound bag. First, determine the distribution of $K$, the sum of three 1-pound bags, then compute $P(Y > W)$, where $Y$ is the weight of a 3-pound bag.

**5.5-8.** Let $X$ denote the wing length in millimeters of a male gallinule and assume that $X\sim N(84.09, 39.37)$ and the wing length $Y$ of a female gallinule is $N(71.93, 50.88)$ and that $X$ and $Y$ are independent. If a male and female gallinule are captured, what is the probability that $X$ is greater than $Y$?

**5.5-9.** Suppose that the length of life in hours (say, $X$) of a light bulb manufactured by company $A$ is $N(800, 14400)$ and the length of life in hours (say, $Y$) of a light bulb manufactured by company $B$ is $N(850, 22500)$. One bulb is randomly selected from each company and is burned until "dead."
(a) Find the probability that the length of life of the bulb from company $A$ exceeds the length of life of the bulb from company $B$ by at least 15 hours.
(b) Find the probability that at least one of the bulbs "lives" for at least 920 hours.

**5.5-10.** A consumer buys $n$ light bulbs, each of which has a distribution that has a mean of 800 hours, a standard deviation of 100 hours, and a normal distribution. A light bulb is replaced by another as soon as it burns out. Assuming...

(Note: The image cuts off at this

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