# Owning a Pet: Probability and StatisticsAccording to the 2017-2018 National Pet Owners Survey conducted by the American Pet Products Association (APPA), sixty-eight percent of U.S. households own a pet. This statistic is the basis for the following exercise in probability and statistics.### Problem 4: Owning a Pet**Scenario:**If 20 households are selected at random, let $ X $ be the number of households that own a pet. We need to determine if this is a binomial problem. For this situation, identify the number of trials $ n $, and the probability of success $ p $.**Tasks:**a. **Binomial Identification:** - Determine if the scenario represents a binomial distribution. - Identify $ n $ and $ p $ for this problem. \[ X \sim \text{Binomial}(n = \_, p = \_) \]b. **Construct Probability Distribution:** - Use Excel to construct the probability distribution for this data.c. **Calculate Probabilities:** - Find the probability that more than 10 of the 20 households have pets. \[ P(X > 10) = \_ \]d. **Calculate Extreme Probabilities:** - Find the probability that less than 5 or more than 15 of the 20 households have pets. \[ P(X < 5 \text{ or } X > 15) = \_ \]e. **Calculate Intermediate Probabilities:** - Find the probability that between 6 and 14 of the 20 households have pets. \[ P(6 \leq X \leq 14) = \_ \]f. **Mean and Interpretation:** - Calculate the mean $ \mu $ of the distribution. \[ \text{Mean } \mu = \_ \] - Interpretation: $ \mu $ for the distribution tells us \_\_\_\_\_\_\_\_\_. This exercise will help reinforce the concepts of binomial distribution and probability calculations, providing practical applications of these mathematical concepts.

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Description: # Owning a Pet: Probability and StatisticsAccording to the 2017-2018 National Pet Owners Survey conducted by the American Pet Products Association (APPA), sixty-eight percent of U.S. households own a pet. This statistic is the basis for the followin

Yes, it's a binomial distribution as it follows the following conditions. Fixed number of trials…

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a. If 20 households are selected at random, let X be the number of households who own a pet. Determine if this is a binomial problem. Identify the number of trials, n, and the probability of success, p, for this problem: 1. 2. 3. 4. X-Binomial ( n= b. Using excel, construct the probability distribution for this data. c. Find the probability that more than 10 of the 20 households have pets. P( d. Find the probability that less than 5 or more than 15 of the 20 households have pets. P( %3D e. Find the probability that between 6 and 14 of the 20 households have pets. P(. f. mean Interpretation: H for the distribution tells us:

a. If 20 households are selected at random, let X be the number of households who own a pet. Determine if this is a binomial problem. Identify the number of trials, n, and the probability of success, p, for this problem: 1. 2. 3. 4. X-Binomial ( n= b. Using excel, construct the probability distribution for this data. c. Find the probability that more than 10 of the 20 households have pets. P( d. Find the probability that less than 5 or more than 15 of the 20 households have pets. P( %3D e. Find the probability that between 6 and 14 of the 20 households have pets. P(. f. mean Interpretation: H for the distribution tells us:

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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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Question

# Owning a Pet: Probability and Statistics

According to the 2017-2018 National Pet Owners Survey conducted by the American Pet Products Association (APPA), sixty-eight percent of U.S. households own a pet. This statistic is the basis for the following exercise in probability and statistics.

### Problem 4: Owning a Pet

**Scenario:**
If 20 households are selected at random, let $ X $ be the number of households that own a pet. We need to determine if this is a binomial problem. For this situation, identify the number of trials $ n $, and the probability of success $ p $.

**Tasks:**

a. **Binomial Identification:**
- Determine if the scenario represents a binomial distribution.
- Identify $ n $ and $ p $ for this problem.

\[
X \sim \text{Binomial}(n = \_, p = \_)
\]

b. **Construct Probability Distribution:**
- Use Excel to construct the probability distribution for this data.

c. **Calculate Probabilities:**
- Find the probability that more than 10 of the 20 households have pets.

\[
P(X > 10) = \_
\]

d. **Calculate Extreme Probabilities:**
- Find the probability that less than 5 or more than 15 of the 20 households have pets.

\[
P(X < 5 \text{ or } X > 15) = \_
\]

e. **Calculate Intermediate Probabilities:**
- Find the probability that between 6 and 14 of the 20 households have pets.

\[
P(6 \leq X \leq 14) = \_
\]

f. **Mean and Interpretation:**
- Calculate the mean $ \mu $ of the distribution.

\[
\text{Mean } \mu = \_
\]
- Interpretation: $ \mu $ for the distribution tells us \_\_\_\_\_\_\_\_\_.

This exercise will help reinforce the concepts of binomial distribution and probability calculations, providing practical applications of these mathematical concepts.

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