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A survey showed that 70% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 7 adults are randomly selected, find the probability that exactly 2 of them need correction for their eyesight. Hint, use the Binomial Distribution formula. 01 0.113 0.00357 0.025

A survey showed that 70% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 7 adults are randomly selected, find the probability that exactly 2 of them need correction for their eyesight. Hint, use the Binomial Distribution formula. 01 0.113 0.00357 0.025

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 and Binomial Distribution **Problem:** A survey showed that 70% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. **Question:** If 7 adults are randomly selected, find the probability that exactly 2 of them need correction for their eyesight. **Hint:** Use the Binomial Distribution formula. **Options:** - □ 1 - □ 0.113 - □ 0.00357 - □ 0.025 **Explanation:** Using the Binomial Distribution formula is essential here. The binomial probability formula is: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] where: - \( n = 7 \) (number of trials) - \( k = 2 \) (number of successes we are looking for) - \( p = 0.70 \) (probability of success on an individual trial) - \( \binom{n}{k} \) is the binomial coefficient, calculated as \(\frac{n!}{k!(n-k)!}\) Plugging in these values will give the probability that exactly 2 out of 7 adults need correction for their eyesight. **Note:** There are no graphs or diagrams in this problem, only textual information and mathematical concepts.
Transcribed Image Text:### Probability and Binomial Distribution **Problem:** A survey showed that 70% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. **Question:** If 7 adults are randomly selected, find the probability that exactly 2 of them need correction for their eyesight. **Hint:** Use the Binomial Distribution formula. **Options:** - □ 1 - □ 0.113 - □ 0.00357 - □ 0.025 **Explanation:** Using the Binomial Distribution formula is essential here. The binomial probability formula is: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] where: - \( n = 7 \) (number of trials) - \( k = 2 \) (number of successes we are looking for) - \( p = 0.70 \) (probability of success on an individual trial) - \( \binom{n}{k} \) is the binomial coefficient, calculated as \(\frac{n!}{k!(n-k)!}\) Plugging in these values will give the probability that exactly 2 out of 7 adults need correction for their eyesight. **Note:** There are no graphs or diagrams in this problem, only textual information and mathematical concepts.
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