Exercise 5-49 Algo (Use computer) Suppose 53% of recent college graduates plan o
ID: 3040435 • Letter: E
Question
Exercise 5-49 Algo
(Use computer) Suppose 53% of recent college graduates plan on pursuing a graduate degree. Twelve recent college graduates are randomly selected.
What is the probability that no more than three of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)
What is the probability that exactly seven of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)
What is the probability that at least six but no more than eleven of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)
(Use computer) Suppose 53% of recent college graduates plan on pursuing a graduate degree. Twelve recent college graduates are randomly selected.
Explanation / Answer
Given that 53% of recent college graduates plan on pursuing a graduate degree => Probability that a recent college graduate plan on pursuing a graduate degree = 0.53
No of recent college graduates selected i.e n = 12
let X denote the no of college graduates who plan on pursuing a graduate degree
formula for Binomial distribution i,e P(X=n) = nCrpr(1-p)n-r
a)Probability that no more than three of the college graduates plan to pursue a graduate degree = P(X=0)+P(X=1)+P(X=2)+P(X=3)
= 12C00.530(1-0.53)12-0 +12C10.531(1-0.53)12-1 + 12C20.532(1-0.53)12-2 + 12C30.533(1-0.53)12-3
= 0.048
b)
probability that exactly seven of the college graduates plan to pursue a graduate degree
= 12C70.537(1-0.53)12-7
= 0.2134
c)
probability that at least six but no more than eleven of the college graduates plan to pursue a graduate degree
= P(6<=X<11)
= P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)
= 12C60.536(1-0.53)12-6+ 12C70.537(1-0.53)12-7+ 12C80.538(1-0.53)12-8+ 12C90.539(1-0.53)12-9
+ 12C100.5310(1-0.53)12-10
= 0.4647