73% of college students prefer in-class learning to online learning. Suppose we randomly select 100 college students and ask them about their in-class vs. online preference. Let X be the number of these students who prefer in-class learning. Let p = the probability of a particular single student preferring in- class learning. a.What is the value of p as a decimal? b. What is the probability that X -71? c. What is the probability that X < 79? d. What is the probability that X > 79? e. What is the expected value of X? f. What is the expected value of X- 5? g. What is the standard deviation of X - 5? h. What is the probability that X is within 2.0 standard deviations of its expected value? i. What is the expected value of 0.73X? j. What is the variance of 0.73X? Add any comments below.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question
73% of college students prefer in-class learning to online learning. Suppose we randomly select 100 college students and ask them about their in-class vs.
online preference. Let X be the number of these students who prefer in-class learning. Let p = the probability of a particular single student preferring in-
class learning.
a.What is the value of p as a decimal?
b. What is the probability that X =71?
c. What is the probability that X < 79?
d. What is the probability that X > 79?
e. What is the expected value of X?
f. What is the expected value of X- 5?
g. What is the standard deviation of X - 5?
h. What is the probability that X is within 2.0 standard deviations of its expected value?
i. What is the expected value of 0.73X?
j. What is the variance of 0.73X?
Add any comments below.
P Type here to search
530 PM
10/1/2020
144
Transcribed Image Text:73% of college students prefer in-class learning to online learning. Suppose we randomly select 100 college students and ask them about their in-class vs. online preference. Let X be the number of these students who prefer in-class learning. Let p = the probability of a particular single student preferring in- class learning. a.What is the value of p as a decimal? b. What is the probability that X =71? c. What is the probability that X < 79? d. What is the probability that X > 79? e. What is the expected value of X? f. What is the expected value of X- 5? g. What is the standard deviation of X - 5? h. What is the probability that X is within 2.0 standard deviations of its expected value? i. What is the expected value of 0.73X? j. What is the variance of 0.73X? Add any comments below. P Type here to search 530 PM 10/1/2020 144
Expert Solution
Step 1

Given that :

73% of college students prefer in-class learning. A sample of 100 college students was taken and their preference was noted.

Also, let X : number of students those who prefer in-class learning over online learning

              p: the probability that a  student prefers in-class learning.

 

(a) Therefore, the value of p (which is same as the proportion of college students preferring in-class learning) as a decimal is : 0.73

 

(b) The probability that X=71 can be modelled using a binomial distribution given as : 

P(X=x) = Cxn px (1-p )n-x,                                  n: number of trials =100                             p : proability of success = 0.73                               x: number of successes  

 

therefore, 

P(X = 71) = C71100 (0.73)x (1-0.73 )100-71                   =  0.07930

 

 

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON