Of students ages 16 to 18 with A or B averages who plan to attend college after graduation, 78% cheated to get higher grades (Source: “Who’s Who Among American High Schools Students”). Ten randomly chosen students with A or B averages that plan to attend college after graduation were asked, “Did you cheat to get higher grades?” What is the probability that exactly four students answered no? Round to the nearest thousandth

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Of students ages 16 to 18 with A or B averages who plan to attend college after
graduation, 78% cheated to get higher grades (Source: “Who’s Who Among American High Schools Students”). Ten randomly chosen students with A or B averages that plan to attend college after graduation were asked, “Did you cheat to get higher grades?”
What is the probability that exactly four students answered no?

Round to the nearest thousandth

Expert Solution
Given

Probability that a student cheated to get higher grades : q = 0.78Therefore, Probability that a student didn't cheat to get higher grades : p = 1-q = 0.22

 

number of students asked if cheated to get higher grades :  n = 10number of studentsfound who didn't cheat : x = 4Therefore, X ~ Bin( n = 10, p = 0.22)where, P(X=x) = Cxn px q(n-x)                          , q = 1-pn: number of trialsp: probability of succesq: probability of failurx: number of successesTo find:the probability that exactly four students answered that they didn't cheat 

 

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