Part: 4 / 6 Part 5 of 6 Find the probability that more than 31% of the freshmen in the sample of 120 are planning to major in a STEM discipline. The probability that more than 31% of the freshmen in the sample of 120 are planning to major in a STEM discipline is X
Part: 4 / 6 Part 5 of 6 Find the probability that more than 31% of the freshmen in the sample of 120 are planning to major in a STEM discipline. The probability that more than 31% of the freshmen in the sample of 120 are planning to major in a STEM discipline is X
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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Part 5
![**Future Scientists: Educational Statistics on STEM Disciplines**
**Background:**
Education professionals refer to science, technology, engineering, and mathematics as the STEM disciplines. A research group reported that 26% of freshmen entering college in a recent year planned to major in a STEM discipline. A random sample of 95 freshmen is selected. The following calculations demonstrate probabilities related to this scenario, rounded to at least four decimal places.
---
**Part 1 of 6:**
Is it appropriate to use the normal approximation to find the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline?
- It **is** appropriate to use the normal curve, since \( np = 24.7 \geq 10 \) and \( n(1 - p) = 70.3 \geq 10 \).
**Part 2 of 6:**
Find the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline.
- The probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline is **0.6700**.
---
**Part 3 of 6:**
A new sample of 120 freshmen is selected. Find the probability that less than 28% of the freshmen in this new sample are planning to major in a STEM discipline.
- The probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline is **0.6915**.
**Part 4 of 6:**
Find the probability that the proportion of freshmen in the sample of 120 who plan to major in a STEM discipline is between 0.32 and 0.38.
- The probability that the proportion of individuals in the sample of 120 who plan to major in a STEM discipline is between 0.32 and 0.38 is **0.0656**.
*[There is a progress bar showing completion of 4 out of 6 parts with a note for Part 5 pending answers.]*
**Part 5 of 6:**
Find the probability that more than 31% of the freshmen in the sample of 120 are planning to major in a STEM discipline.
- The probability that more than 31% of the freshmen in the sample of 120 are planning to major in a STEM discipline is \(___\).
*[An input section is waiting](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe67a4001-a6ff-4bd3-8f91-ff24e2266284%2F0a22c3bd-7e89-40fd-b220-936d2d40272b%2Fjahlyh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Future Scientists: Educational Statistics on STEM Disciplines**
**Background:**
Education professionals refer to science, technology, engineering, and mathematics as the STEM disciplines. A research group reported that 26% of freshmen entering college in a recent year planned to major in a STEM discipline. A random sample of 95 freshmen is selected. The following calculations demonstrate probabilities related to this scenario, rounded to at least four decimal places.
---
**Part 1 of 6:**
Is it appropriate to use the normal approximation to find the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline?
- It **is** appropriate to use the normal curve, since \( np = 24.7 \geq 10 \) and \( n(1 - p) = 70.3 \geq 10 \).
**Part 2 of 6:**
Find the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline.
- The probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline is **0.6700**.
---
**Part 3 of 6:**
A new sample of 120 freshmen is selected. Find the probability that less than 28% of the freshmen in this new sample are planning to major in a STEM discipline.
- The probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline is **0.6915**.
**Part 4 of 6:**
Find the probability that the proportion of freshmen in the sample of 120 who plan to major in a STEM discipline is between 0.32 and 0.38.
- The probability that the proportion of individuals in the sample of 120 who plan to major in a STEM discipline is between 0.32 and 0.38 is **0.0656**.
*[There is a progress bar showing completion of 4 out of 6 parts with a note for Part 5 pending answers.]*
**Part 5 of 6:**
Find the probability that more than 31% of the freshmen in the sample of 120 are planning to major in a STEM discipline.
- The probability that more than 31% of the freshmen in the sample of 120 are planning to major in a STEM discipline is \(___\).
*[An input section is waiting
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