Binomial Distribution Calculatc Ayla Ozturk HW Score: 62.5%, 5 of 8 points Question 6, 6.2.35-T Part 2 of 9 Homework: Section 6.2 O Points: 0 of 1 According to an airline, flights on a certain route are on time 85% of the time. Suppose 10 flights are randomly selected and the on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Find and interpret the probability that exactly 7 flights are on time. (c) Find and interpret the probability that fewer than 7 flights are on time. (d) Find and interpret the probability that at least 7 flights are on time. of (e) Find and interpret the probability that between 5 and 7 flights, inclusive, are on time. of YE. The experiment is performed a fixed number of times. The experiment is performed until a desired number of successes is reached. y of G. The probability of success is the same for each trial of the experiment. y of (b) The probability that exactly 7 flights are on time is (Round to four decimal places as needed.) Help me solve this View an example Get more help. Check ans eakfast Favorites You Want for Just $8.99. Random Nur Sample Size Applebee's Grill + Bar Correlation Co Adventure Park Chuck E. Cheese e info Critical Value X Homework P Do Homework - Section 6.2 - Google Chrome mylab.pearson.com Math 021 Summer 2022 GREEN ACRES (198) Directions lamp liter inn. Savo Mat Clear all 06/13/22 11:12 P

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### Math 021 Summer 2022

#### Homework: Section 6.2

**Question 6, 6.2.35-T (Part 2 of 9)**

---

**Scenario:**
According to an airline, flights on a certain route are on time 85% of the time. Suppose 10 flights are randomly selected and the number of on-time flights is recorded.

**Questions:**
(a) Explain why this is a binomial experiment.  
(b) Find and interpret the probability that exactly 7 flights are on time.  
(c) Find and interpret the probability that fewer than 7 flights are on time.  
(d) Find and interpret the probability that at least 7 flights are on time.  
(e) Find and interpret the probability that between 5 and 7 flights, inclusive, are on time.

---

**Hints:**

1. The experiment is performed a fixed number of times.
2. The experiment is performed until a desired number of successes is reached.
3. The probability of success is the same for each trial of the experiment.

---

**Solution Framework:**

**(a)**  
Explanation of why this is a binomial experiment:
- The number of trials is fixed (10 flights).
- There are only two possible outcomes for each trial (on time or not on time).
- The probability of success (an on-time flight) is the same for each trial (85% or 0.85).

**(b)**  
The probability that exactly 7 flights are on time:
- Use the binomial probability formula to calculate.

**(c)**  
The probability that fewer than 7 flights are on time:
- Use the cumulative binomial probability formula or subtract the probabilities of having more than 7 flights on time from 1.

**(d)**  
The probability that at least 7 flights are on time:
- Use the cumulative binomial probability formula or subtract the probabilities of having fewer than 7 flights on time from 1.

**(e)**  
The probability that between 5 and 7 flights, inclusive, are on time:
- Calculate the individual probabilities for 5, 6, and 7 flights being on time and sum them up.

The binomial probability formula is:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
where:
- \( n \) is the number of trials
Transcribed Image Text:--- ### Math 021 Summer 2022 #### Homework: Section 6.2 **Question 6, 6.2.35-T (Part 2 of 9)** --- **Scenario:** According to an airline, flights on a certain route are on time 85% of the time. Suppose 10 flights are randomly selected and the number of on-time flights is recorded. **Questions:** (a) Explain why this is a binomial experiment. (b) Find and interpret the probability that exactly 7 flights are on time. (c) Find and interpret the probability that fewer than 7 flights are on time. (d) Find and interpret the probability that at least 7 flights are on time. (e) Find and interpret the probability that between 5 and 7 flights, inclusive, are on time. --- **Hints:** 1. The experiment is performed a fixed number of times. 2. The experiment is performed until a desired number of successes is reached. 3. The probability of success is the same for each trial of the experiment. --- **Solution Framework:** **(a)** Explanation of why this is a binomial experiment: - The number of trials is fixed (10 flights). - There are only two possible outcomes for each trial (on time or not on time). - The probability of success (an on-time flight) is the same for each trial (85% or 0.85). **(b)** The probability that exactly 7 flights are on time: - Use the binomial probability formula to calculate. **(c)** The probability that fewer than 7 flights are on time: - Use the cumulative binomial probability formula or subtract the probabilities of having more than 7 flights on time from 1. **(d)** The probability that at least 7 flights are on time: - Use the cumulative binomial probability formula or subtract the probabilities of having fewer than 7 flights on time from 1. **(e)** The probability that between 5 and 7 flights, inclusive, are on time: - Calculate the individual probabilities for 5, 6, and 7 flights being on time and sum them up. The binomial probability formula is: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] where: - \( n \) is the number of trials
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