3. It is reported that 85% of all freshman entering high school graduate on time with their class. A random sample of 145 freshmen are selected. a. Find the mean . 85± 145 0,59 0159 = 145 f = 24121046x c. Find the probability that less than 80% of freshmen in the sample graduated. b. Find the standard deviation op.
3. It is reported that 85% of all freshman entering high school graduate on time with their class. A random sample of 145 freshmen are selected. a. Find the mean . 85± 145 0,59 0159 = 145 f = 24121046x c. Find the probability that less than 80% of freshmen in the sample graduated. b. Find the standard deviation op.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![### Transcription for Educational Website
#### Statistical Analysis of Freshman Graduation Rates
**Problem Statement:**
3. It is reported that 85% of all freshmen entering high school graduate on time with their class. A random sample of 145 freshmen is selected.
**Tasks:**
a. **Find the Mean, \( \mu_p \):**
- The mean graduation rate is given as 85%, which is represented as \( f = 0.85 \).
- Sample size (\( n \)) = 145.
b. **Find the Standard Deviation, \( \sigma_p \):**
- Calculate the standard deviation using the formula for a sample proportion:
\[
\sigma_p = \sqrt{\frac{f(1 - f)}{n}}
\]
- Substitution:
\[
\sigma_p = \sqrt{\frac{0.85 \times 0.15}{145}} \approx 0.059
\]
c. **Find the Probability that Less than 80% of Freshmen in the Sample Graduated:**
- Use the z-score formula to find the probability:
\[
z = \frac{p - \mu_p}{\sigma_p}
\]
where \( p = 0.80 \).
- Calculation of z-score:
\[
z = \frac{0.80 - 0.85}{0.059} \approx -1.81
\]
**Note:**
- The text includes some handwritten calculations which confirm the steps mentioned.
- There are no graphs or diagrams present in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ee5d418-4908-4b12-8875-38434e326383%2Fbee1e55e-bda6-4539-a0a7-80597d588640%2Ffd1g993_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Transcription for Educational Website
#### Statistical Analysis of Freshman Graduation Rates
**Problem Statement:**
3. It is reported that 85% of all freshmen entering high school graduate on time with their class. A random sample of 145 freshmen is selected.
**Tasks:**
a. **Find the Mean, \( \mu_p \):**
- The mean graduation rate is given as 85%, which is represented as \( f = 0.85 \).
- Sample size (\( n \)) = 145.
b. **Find the Standard Deviation, \( \sigma_p \):**
- Calculate the standard deviation using the formula for a sample proportion:
\[
\sigma_p = \sqrt{\frac{f(1 - f)}{n}}
\]
- Substitution:
\[
\sigma_p = \sqrt{\frac{0.85 \times 0.15}{145}} \approx 0.059
\]
c. **Find the Probability that Less than 80% of Freshmen in the Sample Graduated:**
- Use the z-score formula to find the probability:
\[
z = \frac{p - \mu_p}{\sigma_p}
\]
where \( p = 0.80 \).
- Calculation of z-score:
\[
z = \frac{0.80 - 0.85}{0.059} \approx -1.81
\]
**Note:**
- The text includes some handwritten calculations which confirm the steps mentioned.
- There are no graphs or diagrams present in the image.
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