Q45. The probability that it will rain on any one day during the month of May is 0.15. There are 31 days in May. Assuming independence, what is the probability that it will rain 10 days or fewer in May? A. 0.0011 B. 0.2214 C. 0.7866 D. 0.9961 E. 0.9989
Q45. The probability that it will rain on any one day during the month of May is 0.15. There are 31 days in May. Assuming independence, what is the probability that it will rain 10 days or fewer in May? A. 0.0011 B. 0.2214 C. 0.7866 D. 0.9961 E. 0.9989
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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![### Probability Question
**Q45.** The probability that it will rain on any one day during the month of May is 0.15. There are 31 days in May. Assuming independence, what is the probability that it will rain 10 days or fewer in May?
**Options:**
A. 0.0011
B. 0.2214
C. 0.7866
D. 0.9961
E. 0.9989
### Explanation:
This problem involves calculating the cumulative probability of a binomial random variable. The binomial distribution is appropriate because we have a fixed number of trials (31 days), two possible outcomes (rain or no rain), a constant probability of rain on each day (0.15), and independence of the trials. The probability that it will rain on exactly \( k \) days out of 31 can be computed using the binomial probability formula:
\[ P(X = k) = \binom{31}{k} (0.15)^k (0.85)^{31-k} \]
Where \(\binom{31}{k}\) is the binomial coefficient. The cumulative probability that it will rain 10 days or fewer is the sum of the probabilities that it will rain on exactly 0, 1, 2, ..., 10 days.
Due to the complexity of manual computation, this cumulative probability is typically found using statistical tables or software designed to compute binomial probabilities. Answers to such problems can be found using statistical tools like R, Python, or a binomial cumulative probability table.
The correct answers for this question are included in the provided multiple-choice options and require computation or lookup for verification.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40d81c3d-217c-474a-b6c2-74f4c4a8c8c0%2Fa2884899-18bd-4c3b-ba62-40b0f6f26f90%2F5d6670p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Question
**Q45.** The probability that it will rain on any one day during the month of May is 0.15. There are 31 days in May. Assuming independence, what is the probability that it will rain 10 days or fewer in May?
**Options:**
A. 0.0011
B. 0.2214
C. 0.7866
D. 0.9961
E. 0.9989
### Explanation:
This problem involves calculating the cumulative probability of a binomial random variable. The binomial distribution is appropriate because we have a fixed number of trials (31 days), two possible outcomes (rain or no rain), a constant probability of rain on each day (0.15), and independence of the trials. The probability that it will rain on exactly \( k \) days out of 31 can be computed using the binomial probability formula:
\[ P(X = k) = \binom{31}{k} (0.15)^k (0.85)^{31-k} \]
Where \(\binom{31}{k}\) is the binomial coefficient. The cumulative probability that it will rain 10 days or fewer is the sum of the probabilities that it will rain on exactly 0, 1, 2, ..., 10 days.
Due to the complexity of manual computation, this cumulative probability is typically found using statistical tables or software designed to compute binomial probabilities. Answers to such problems can be found using statistical tools like R, Python, or a binomial cumulative probability table.
The correct answers for this question are included in the provided multiple-choice options and require computation or lookup for verification.
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