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.
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)
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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.
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10/1/2020
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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 :
therefore,
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