Question

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities. Fifty dash two percent of adults say that they have cheated on a test or exam before. You randomly select six adults. Find the probability that the number of adults who say that they have cheated on a test or exam before is​ (a) exactly four​, ​(b) more than two​, and​ (c) at most five. ​(a) Upper P left parenthesis 4 right parenthesisequals nothing ​(Round to three decimal places as​ needed.) ​(b) Upper P left parenthesis more than two right parenthesisequals nothing ​(Round to three decimal places as​ needed.) ​(c) Upper P left parenthesis at most five right parenthesisequals nothing ​(Round to three decimal places as​ needed.) Which of the events are​ unusual? Select all that apply. A. The event Upper P left parenthesis 4 right parenthesis is unusual. B. The event Upper P left parenthesis more than two right parenthesis is unusual. C. The event Upper P left parenthesis at most five right parenthesis is unusual. D. None of the events are unusual.

Answer 1

Ans:

Use binomial distribution with n=6 and p=0.52

P(x=k)=⁶C_k*0.52*(1-0.52)^6-k

x	P(x)
0	0.0122
1	0.0795
2	0.2153
3	0.3110
4	0.2527
5	0.1095
6	0.0198

a)

P(x=4)=⁶C₄*0.52^4*0.48^2=0.2527

b)

P(x>2)=1-P(x=0)-P(x=1)-P(x=2)

=1-(1-0.52)^6-⁶C₁*0.52*(1-0.52)^5-⁶C₂*0.52^2*(1-0.52)^4

=0.6930

c)

P(at most 5)=P(x<=5)=1-P(x=6)

=1-0.52^6=0.9802

Option D is correct.

None of the events are unusual.

(as all probabilities are greater than 0.05)