30% of all college students major in STEM (Science, Technology, Engineering, and Math). If 34 college students are randomly selected, find the probability that exactly 10 of them major in STEM. Round to 4 decimal places.
30% of all college students major in STEM (Science, Technology, Engineering, and Math). If 34 college students are randomly selected, find the probability that exactly 10 of them major in STEM. Round to 4 decimal places.
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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![**Probability Problem in STEM Education**
30% of all college students major in STEM (Science, Technology, Engineering, and Math). If 34 college students are randomly selected, find the probability that exactly 10 of them major in STEM.
**Solution Details**
To solve this problem, one would typically use the binomial probability formula, given by:
\[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \]
Where:
- \( n \) is the number of trials (in this case, 34).
- \( k \) is the number of successful outcomes (in this case, 10).
- \( p \) is the probability of success on a single trial (in this case, 0.3).
- \( \binom{n}{k} \) is the number of combinations of n items taken k at a time.
**Instructions for Calculation**
Complete the calculation using the given values and round your answer to 4 decimal places.
(Note: There are no graphs or diagrams provided in the image. If any calculations further require graphical representation, please refer to tools or software capable of performing statistical plot functions.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11f84057-ddc6-4a16-833f-eeebb801b1ce%2Fdb2c94a4-ad61-4712-8736-529811736db5%2F2ecfz79_processed.png&w=3840&q=75)
Transcribed Image Text:**Probability Problem in STEM Education**
30% of all college students major in STEM (Science, Technology, Engineering, and Math). If 34 college students are randomly selected, find the probability that exactly 10 of them major in STEM.
**Solution Details**
To solve this problem, one would typically use the binomial probability formula, given by:
\[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \]
Where:
- \( n \) is the number of trials (in this case, 34).
- \( k \) is the number of successful outcomes (in this case, 10).
- \( p \) is the probability of success on a single trial (in this case, 0.3).
- \( \binom{n}{k} \) is the number of combinations of n items taken k at a time.
**Instructions for Calculation**
Complete the calculation using the given values and round your answer to 4 decimal places.
(Note: There are no graphs or diagrams provided in the image. If any calculations further require graphical representation, please refer to tools or software capable of performing statistical plot functions.)
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