### Probability Analysis of Smartphone Upgrades**4. Gallup Poll Insights on U.S. Smartphone Users**According to a recent national Gallup Poll of U.S. smartphone users, 57% upgrade their cell phone every two years. Use this information to answer the following questions. **Show all work.** Be sure to include your probability and calculator statements for the questions where indicated.**Instructions:**Determine the probability (to 4 decimal places) for each of the following scenarios:- (Actual questions follow this introductory section, prompting for various probability calculations related to smartphone upgrades based on the given 57% upgrade rate every two years.) ### Probability Exercise: Cell Phone Upgrade Frequency#### Problem Statement**A.** Exactly 8 users out of 15 smartphone users do not upgrade their cell phones every two years.#### Instructions1. **Probability Statement:** State the question using probability notation: $ P( \quad ) $2. **Calculator Function with Values:** List the TI calculator function with values used to solve this problem.#### Detailed ExplanationTo solve this probability problem, we need to understand and correctly notate it. The probability of exactly 8 users out of 15 not upgrading their cell phones could be expressed in terms of binomial probability. ### Probability Notation\[ P(X = 8) \]**Where:**- $ X $ is the random variable representing the number of users who do not upgrade their cell phones.- $ P(X = 8) $ signifies the probability that exactly 8 out of the 15 users fall into this category.### Calculator FunctionFor solving this, a TI calculator (like TI-83 or TI-84) can be used. The function generally used for binomial probability is:\[ binompdf(n, p, k) \]**Where:**- $ n $ is the number of trials (15 users).- $ p $ is the probability of success on a single trial (assuming a known probability of not upgrading).- $ k $ is the number of successes (in this case, 8 users).### Example CalculationIf the probability of an individual not upgrading their phone every two years is known (say $ p = 0.5 $), you would plug the values into the calculator as follows:\[ binompdf(15, 0.5, 8) \]Use these steps and notation to work through the probability problem effectively.

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Description: ### Probability Analysis of Smartphone Upgrades**4. Gallup Poll Insights on U.S. Smartphone Users**According to a recent national Gallup Poll of U.S. smartphone users, 57% upgrade their cell phone every two years. Use this information to answer the

The given information is that, 57% of U.S. smartphone users upgrade their cell phone every two…

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exactly 8 users out of 15 smartphone users do not upgrade their cell phones every two years. Probability statement: [State question using probability notation: P( )I Calculator Function w/values: [List TI calculator function with values used to solve this problem.]

exactly 8 users out of 15 smartphone users do not upgrade their cell phones every two years. Probability statement: [State question using probability notation: P( )I Calculator Function w/values: [List TI calculator function with values used to solve this problem.]

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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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### Probability Analysis of Smartphone Upgrades

**4. Gallup Poll Insights on U.S. Smartphone Users**
According to a recent national Gallup Poll of U.S. smartphone users, 57% upgrade their cell phone every two years. Use this information to answer the following questions. **Show all work.** Be sure to include your probability and calculator statements for the questions where indicated.

**Instructions:**
Determine the probability (to 4 decimal places) for each of the following scenarios:

- (Actual questions follow this introductory section, prompting for various probability calculations related to smartphone upgrades based on the given 57% upgrade rate every two years.)

### Probability Exercise: Cell Phone Upgrade Frequency

#### Problem Statement
**A.** Exactly 8 users out of 15 smartphone users do not upgrade their cell phones every two years.

#### Instructions
1. **Probability Statement:**
State the question using probability notation: $ P( \quad ) $

2. **Calculator Function with Values:**
List the TI calculator function with values used to solve this problem.

#### Detailed Explanation
To solve this probability problem, we need to understand and correctly notate it. The probability of exactly 8 users out of 15 not upgrading their cell phones could be expressed in terms of binomial probability.

### Probability Notation
\[ P(X = 8) \]

**Where:**
- $ X $ is the random variable representing the number of users who do not upgrade their cell phones.
- $ P(X = 8) $ signifies the probability that exactly 8 out of the 15 users fall into this category.

### Calculator Function
For solving this, a TI calculator (like TI-83 or TI-84) can be used. The function generally used for binomial probability is:

\[ binompdf(n, p, k) \]

**Where:**
- $ n $ is the number of trials (15 users).
- $ p $ is the probability of success on a single trial (assuming a known probability of not upgrading).
- $ k $ is the number of successes (in this case, 8 users).

### Example Calculation
If the probability of an individual not upgrading their phone every two years is known (say $ p = 0.5 $), you would plug the values into the calculator as follows:

\[ binompdf(15, 0.5, 8) \]

Use these steps and notation to work through the probability problem effectively.

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