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Questions 5-8: The chance that you wake up on time on any given day is 35%. Suppose 5 days have gone by, and each day is independent. 5. What is the probability you wake up on time 2 out of the 5 days? (show your work on this one, and a screenshot of how you worked it out on the calculator or excel). 6. What is the probability you wake up on time all 5 days? 7. What is the probability you wake up on time at least one day out of the five? 8. What is the expected number of days, out of 5, that you will wake up on time?

Questions 5-8: The chance that you wake up on time on any given day is 35%. Suppose 5 days have gone by, and each day is independent. 5. What is the probability you wake up on time 2 out of the 5 days? (show your work on this one, and a screenshot of how you worked it out on the calculator or excel). 6. What is the probability you wake up on time all 5 days? 7. What is the probability you wake up on time at least one day out of the five? 8. What is the expected number of days, out of 5, that you will wake up on time?

MATLAB: An Introduction with Applications
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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Help I am confused with binomial distribution

**Probability and Expected Value Problems:** *The following exercises explore probability scenarios with waking up on time.* **Questions 5-8: The chance that you wake up on time on any given day is 35%. Suppose 5 days have gone by, and each day is independent.** 5. **What is the probability you wake up on time 2 out of the 5 days?** (show your work on this one, and a screenshot of how you worked it out on the calculator or Excel) - **To calculate this probability**: Use the binomial probability formula. - **Formula**: \( P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \) - \( n = 5 \), \( k = 2 \), \( p = 0.35 \) - \( \binom{5}{2} = 10 \) - \( P(X = 2) = 10 \times (0.35)^2 \times (0.65)^3 \) 6. **What is the probability you wake up on time all 5 days?** - **Calculation**: \( (0.35)^5 \) - This represents the probability of waking up on time every day for five consecutive days. 7. **What is the probability you wake up on time at least one day out of the five?** - **Formula**: Use complementary probability. - \( P(\text{at least one}) = 1 - P(\text{none}) \) - **Calculation**: \( 1 - (0.65)^5 \) - This calculation finds the probability of waking up on time at least once by subtracting the probability of waking up on time zero times (none) from 1. 8. **What is the expected number of days, out of 5, that you will wake up on time?** - **Formula for expected value**: \( E(X) = n \times p \) - **Calculation**: \( 5 \times 0.35 = 1.75 \) - On average, you can expect to wake up on time approximately 1.75 days out of 5. These exercises provide practice with probability concepts and calculations, exploring both specific and general scenarios about independent daily events.
Transcribed Image Text:**Probability and Expected Value Problems:** *The following exercises explore probability scenarios with waking up on time.* **Questions 5-8: The chance that you wake up on time on any given day is 35%. Suppose 5 days have gone by, and each day is independent.** 5. **What is the probability you wake up on time 2 out of the 5 days?** (show your work on this one, and a screenshot of how you worked it out on the calculator or Excel) - **To calculate this probability**: Use the binomial probability formula. - **Formula**: \( P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \) - \( n = 5 \), \( k = 2 \), \( p = 0.35 \) - \( \binom{5}{2} = 10 \) - \( P(X = 2) = 10 \times (0.35)^2 \times (0.65)^3 \) 6. **What is the probability you wake up on time all 5 days?** - **Calculation**: \( (0.35)^5 \) - This represents the probability of waking up on time every day for five consecutive days. 7. **What is the probability you wake up on time at least one day out of the five?** - **Formula**: Use complementary probability. - \( P(\text{at least one}) = 1 - P(\text{none}) \) - **Calculation**: \( 1 - (0.65)^5 \) - This calculation finds the probability of waking up on time at least once by subtracting the probability of waking up on time zero times (none) from 1. 8. **What is the expected number of days, out of 5, that you will wake up on time?** - **Formula for expected value**: \( E(X) = n \times p \) - **Calculation**: \( 5 \times 0.35 = 1.75 \) - On average, you can expect to wake up on time approximately 1.75 days out of 5. These exercises provide practice with probability concepts and calculations, exploring both specific and general scenarios about independent daily events.
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