### Probability of U.S. Smartphone Users Upgrading#### Problem Statement: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) that:(Note: The detailed questions to be answered are not provided in the image, but you will need to calculate probabilities using the given 57% upgrade rate.)- **Upgrading Probability**: With 57% of users upgrading every two years, consider a binomial distribution scenario.- **Calculations**: Be meticulous with each step. Include all probability and calculator functions used.Please proceed with solving and explaining the questions based on the given probability information in a clear and detailed manner. **Probability of Smartphone Users Not Upgrading Their Cell Phones**In this example, we are determining the probability that at least 1 user out of 15 smartphone users does not upgrade their cell phones every two years.**Probability Statement:**To express this in probability notation, we use the following representation:\[ P(\text{at least 1 user does not upgrade}) \]**Calculator Function with Values:**To calculate the required probability using a TI calculator, we will input the relevant function and values. Here we will list the specific TI calculator function along with the appropriate values that need to be used for this calculation. **Step-by-Step Explanation:**1. **Defining the Event**: The event of interest is "at least 1 user out of 15 doesn’t upgrade their cell phone every 2 years."2. **Understanding the Complement**: We can use the complement rule to simplify the computation: \[ P(\text{at least 1 user does not upgrade}) = 1 - P(\text{all 15 users upgrade}) \]3. **Calculating the Complement**: - First, determine the probability that a single user upgrades their cell phone. - Then, calculate the probability that all 15 users upgrade their cell phones.4. **TI Calculator Function**: - Use the appropriate binomial or probability distribution function provided by the TI calculator. List the specific function (e.g., binomial probability, cumulative distribution) and the exact values that need to be input.For this particular example, one might use the binomial cumulative distribution function on the TI calculator as follows (assuming the probability of not upgrading is known):\[ P(X \geq 1) = 1 - P(X = 0) \]In the TI calculator, you might use:\[ P(\text{binomcdf}(n = 15, \text{probability of not upgrading}, x = 0)) \]This completes the setup for determining the probability that at least 1 out of 15 smartphone users does not upgrade their cell phones every two years using probability notation and a TI calculator.

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

D. at least 1 user out of the 15 smartphone users do not upgrade their cell phones every two years. Probability statement: (State question using probability notation: P( )) Calculator Function w/values: (List TI calculator function with values used

D. at least 1 user out of the 15 smartphone users do not upgrade their cell phones every two years. Probability statement: (State question using probability notation: P( )) Calculator Function w/values: (List TI calculator function with values used

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

### Probability of U.S. Smartphone Users Upgrading

#### Problem Statement:
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) that:

(Note: The detailed questions to be answered are not provided in the image, but you will need to calculate probabilities using the given 57% upgrade rate.)

- **Upgrading Probability**: With 57% of users upgrading every two years, consider a binomial distribution scenario.
- **Calculations**: Be meticulous with each step. Include all probability and calculator functions used.

Please proceed with solving and explaining the questions based on the given probability information in a clear and detailed manner.

**Probability of Smartphone Users Not Upgrading Their Cell Phones**

In this example, we are determining the probability that at least 1 user out of 15 smartphone users does not upgrade their cell phones every two years.

**Probability Statement:**

To express this in probability notation, we use the following representation:

\[ P(\text{at least 1 user does not upgrade}) \]

**Calculator Function with Values:**

To calculate the required probability using a TI calculator, we will input the relevant function and values. Here we will list the specific TI calculator function along with the appropriate values that need to be used for this calculation.

**Step-by-Step Explanation:**

1. **Defining the Event**: The event of interest is "at least 1 user out of 15 doesn’t upgrade their cell phone every 2 years."

2. **Understanding the Complement**: We can use the complement rule to simplify the computation:
\[ P(\text{at least 1 user does not upgrade}) = 1 - P(\text{all 15 users upgrade}) \]

3. **Calculating the Complement**:
- First, determine the probability that a single user upgrades their cell phone.
- Then, calculate the probability that all 15 users upgrade their cell phones.

4. **TI Calculator Function**:
- Use the appropriate binomial or probability distribution function provided by the TI calculator. List the specific function (e.g., binomial probability, cumulative distribution) and the exact values that need to be input.

For this particular example, one might use the binomial cumulative distribution function on the TI calculator as follows (assuming the probability of not upgrading is known):

\[ P(X \geq 1) = 1 - P(X = 0) \]

In the TI calculator, you might use:

\[ P(\text{binomcdf}(n = 15, \text{probability of not upgrading}, x = 0)) \]

This completes the setup for determining the probability that at least 1 out of 15 smartphone users does not upgrade their cell phones every two years using probability notation and a TI calculator.

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