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a. Exactly 10 of them major in STEM. b. At most 14 of them major in STEM. c. At least 12 of them major in STEM.

a. Exactly 10 of them major in STEM. b. At most 14 of them major in STEM. c. At least 12 of them major in STEM.

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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### Probability of College Students Majoring in STEM **Problem Statement:** 29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 44 college students are randomly selected, find the probability that: a. Exactly 10 of them major in STEM. b. At most 14 of them major in STEM. c. At least 12 of them major in STEM. d. Between 7 and 15 (including 7 and 15) of them major in STEM. **Detailed Explanation (if needed):** - To solve these probability problems, we can use the binomial distribution formula where the number of trials \( n \) is 44 (students) and the probability of success \( p \) is 0.29 (since 29% major in STEM). - For each question: - (a) Use the binomial probability formula to find \( P(X = 10) \). - (b) Find \( P(X \leq 14) \), which is the cumulative probability of \( X \) being 14 or less. - (c) Find \( P(X \geq 12) \), which is the cumulative probability of \( X \) being 12 or more. - (d) Find \( P(7 \leq X \leq 15) \), which requires calculating the cumulative probability between 7 and 15 inclusive. **Note:** Using statistical software or a binomial probability table can assist in finding these probabilities more easily. Alternatively, a calculator with binomial distribution functions can also be used.
Transcribed Image Text:### Probability of College Students Majoring in STEM **Problem Statement:** 29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 44 college students are randomly selected, find the probability that: a. Exactly 10 of them major in STEM. b. At most 14 of them major in STEM. c. At least 12 of them major in STEM. d. Between 7 and 15 (including 7 and 15) of them major in STEM. **Detailed Explanation (if needed):** - To solve these probability problems, we can use the binomial distribution formula where the number of trials \( n \) is 44 (students) and the probability of success \( p \) is 0.29 (since 29% major in STEM). - For each question: - (a) Use the binomial probability formula to find \( P(X = 10) \). - (b) Find \( P(X \leq 14) \), which is the cumulative probability of \( X \) being 14 or less. - (c) Find \( P(X \geq 12) \), which is the cumulative probability of \( X \) being 12 or more. - (d) Find \( P(7 \leq X \leq 15) \), which requires calculating the cumulative probability between 7 and 15 inclusive. **Note:** Using statistical software or a binomial probability table can assist in finding these probabilities more easily. Alternatively, a calculator with binomial distribution functions can also be used.
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