34% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is (a) exactly two, (b) more than two, and (c) between two and five, inclusive. (a) P(2)= (Round to the nearest thousandth as needed.)
34% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is (a) exactly two, (b) more than two, and (c) between two and five, inclusive. (a) P(2)= (Round to the nearest thousandth as needed.)
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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![### Probability in Sales Tax Holiday Purchase Likelihood
**Scenario:**
34% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is:
(a) exactly two,
(b) more than two,
(c) between two and five, inclusive.
**Calculations:**
(a) P(2) = __ (Round to the nearest thousandth as needed).
**Instructions for Students:**
To solve the above problem, you will need to use binomial probability formulas. Here is a quick reminder of the steps involved:
1. **Understanding the Binomial Distribution:**
- **Number of trials (n):** This represents the number of adults selected, which is 10.
- **Probability of success (p):** The probability that an adult is more likely to purchase during a sales tax holiday, which is 0.34.
- **Number of successes (k):** The specific number of adults we are interested in.
2. **Calculating Exact Probability (a):**
Use the binomial probability formula:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
Where \(\binom{n}{k}\) is the binomial coefficient.
In this scenario for exactly 2 adults (k = 2):
\[
P(2) = \binom{10}{2} (0.34)^2 (0.66)^8
\]
3. **Calculating Probability of More Than Two (b):**
This can be calculated by finding the sum of probabilities from 3 to 10:
\[
P(X > 2) = \sum_{k=3}^{10} \binom{10}{k} (0.34)^k (0.66)^{10-k}
\]
4. **Calculating Probability Between Two and Five (c):**
Here we calculate the sum of probabilities from 2 to 5:
\[
P(2 \leq X \leq 5) = \sum_{k=2}^{5} \binom{10}{k} (0.34)^k (0.66)^{10-k](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F216d8975-823a-443e-8abc-06f056adfa09%2F887b69a9-1358-4f75-837b-44c554d61d76%2Fttafkjp_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability in Sales Tax Holiday Purchase Likelihood
**Scenario:**
34% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is:
(a) exactly two,
(b) more than two,
(c) between two and five, inclusive.
**Calculations:**
(a) P(2) = __ (Round to the nearest thousandth as needed).
**Instructions for Students:**
To solve the above problem, you will need to use binomial probability formulas. Here is a quick reminder of the steps involved:
1. **Understanding the Binomial Distribution:**
- **Number of trials (n):** This represents the number of adults selected, which is 10.
- **Probability of success (p):** The probability that an adult is more likely to purchase during a sales tax holiday, which is 0.34.
- **Number of successes (k):** The specific number of adults we are interested in.
2. **Calculating Exact Probability (a):**
Use the binomial probability formula:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
Where \(\binom{n}{k}\) is the binomial coefficient.
In this scenario for exactly 2 adults (k = 2):
\[
P(2) = \binom{10}{2} (0.34)^2 (0.66)^8
\]
3. **Calculating Probability of More Than Two (b):**
This can be calculated by finding the sum of probabilities from 3 to 10:
\[
P(X > 2) = \sum_{k=3}^{10} \binom{10}{k} (0.34)^k (0.66)^{10-k}
\]
4. **Calculating Probability Between Two and Five (c):**
Here we calculate the sum of probabilities from 2 to 5:
\[
P(2 \leq X \leq 5) = \sum_{k=2}^{5} \binom{10}{k} (0.34)^k (0.66)^{10-k
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