A survey showed that 80% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 20 adults are randomly selected, find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight correction? The probability that no more than 1 of the 20 adults require eyesight correction is (Round to three decimal places as needed.)
A survey showed that 80% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 20 adults are randomly selected, find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight correction? The probability that no more than 1 of the 20 adults require eyesight correction is (Round to three decimal places as needed.)
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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Please answer both questions
![### Probability of Eyesight Correction Among Adults
**Survey Insight:**
A survey indicated that 80% of adults require some form of eyesight correction, whether it be through eyeglasses, contact lenses, surgery, or other methods.
**Problem Statement:**
If a group of 20 adults is randomly selected, what is the probability that no more than 1 of these 20 adults will need eyesight correction? Additionally, is having only 1 adult requiring eyesight correction from this group considered a significantly low number?
**Mathematical Problem:**
The probability of no more than 1 out of 20 adults requiring eyesight correction can be determined using statistical methods. Specifically, we will use the binomial probability formula where:
- The probability of an adult needing eyesight correction (\(p\)) is 0.80.
- The probability of an adult not needing eyesight correction (\(q\)) is 1 - 0.80 = 0.20.
- The number of trials (\(n\)) is 20.
The calculation will involve summing the probabilities of exactly 0 and exactly 1 adult needing eyesight correction.
**Result:**
The probability that no more than 1 of the 20 adults require eyesight correction is
\[
P(X \leq 1) = P(X = 0) + P(X = 1)
\]
where \(P(X = k)\) is given by the binomial probability formula:
\[
P(X = k)= \binom{n}{k} p^k q^{n-k}
\]
- For \(k = 0\):
\[
P(X = 0) = \binom{20}{0} (0.80)^0 (0.20)^{20} = 1 \cdot 1 \cdot 0.20^{20}
\]
- For \(k = 1\):
\[
P(X = 1) = \binom{20}{1} (0.80)^1 (0.20)^{19} = 20 \cdot 0.80 \cdot 0.20^{19}
\]
**Conclusion:**
The final probability value should be rounded to three decimal places as needed. Fill in the final calculated value in the empty box provided in your original context.
---
This explanation includes a clear translation of the problem and guides the reader through the necessary steps to understand and solve the statistical](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49a5c0da-d10b-4c66-9f47-a76740d10419%2F24d9184d-6084-4f11-a30b-ec79c14c175a%2Flpq8jq8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability of Eyesight Correction Among Adults
**Survey Insight:**
A survey indicated that 80% of adults require some form of eyesight correction, whether it be through eyeglasses, contact lenses, surgery, or other methods.
**Problem Statement:**
If a group of 20 adults is randomly selected, what is the probability that no more than 1 of these 20 adults will need eyesight correction? Additionally, is having only 1 adult requiring eyesight correction from this group considered a significantly low number?
**Mathematical Problem:**
The probability of no more than 1 out of 20 adults requiring eyesight correction can be determined using statistical methods. Specifically, we will use the binomial probability formula where:
- The probability of an adult needing eyesight correction (\(p\)) is 0.80.
- The probability of an adult not needing eyesight correction (\(q\)) is 1 - 0.80 = 0.20.
- The number of trials (\(n\)) is 20.
The calculation will involve summing the probabilities of exactly 0 and exactly 1 adult needing eyesight correction.
**Result:**
The probability that no more than 1 of the 20 adults require eyesight correction is
\[
P(X \leq 1) = P(X = 0) + P(X = 1)
\]
where \(P(X = k)\) is given by the binomial probability formula:
\[
P(X = k)= \binom{n}{k} p^k q^{n-k}
\]
- For \(k = 0\):
\[
P(X = 0) = \binom{20}{0} (0.80)^0 (0.20)^{20} = 1 \cdot 1 \cdot 0.20^{20}
\]
- For \(k = 1\):
\[
P(X = 1) = \binom{20}{1} (0.80)^1 (0.20)^{19} = 20 \cdot 0.80 \cdot 0.20^{19}
\]
**Conclusion:**
The final probability value should be rounded to three decimal places as needed. Fill in the final calculated value in the empty box provided in your original context.
---
This explanation includes a clear translation of the problem and guides the reader through the necessary steps to understand and solve the statistical
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