Question

Consider a binomial probability distribution with p 0.3 and n 8. What is the probability of the following? a b) exactly three successes less than three successes six or more successes a) P(x 3) 0.2541 (Round to four decimal places as needed.) b) P(x 3)= 0.5518 (Round to four decimal places as needed.) c) P(x 6) 0.0113 (Round to four decimal places as needed.)

The answers are in red. Please do part a-c. Thanks!

Answer 1

Probability

Solution: a. From the given information, X follows binomial distribution with n=8 and p =0.3. Then. P(X =3) = ($)(0.3)*(1-0,3)* = 56x0.33 0.75 =0.2541 P(X<3)= P(X =0)+P( X =1)+P( X = 2) - (0)(0.3°(1–03)*°+)(0.3)(1-0.33* +(9](03)*(1-03)** = 0.0576+0.1977 +0.2965 = 0.5518

P(X26) = P(X = 6)+P(X = 7) + P(X = 8) -6)(0.3)*(1-0,3)** +(9]603) (1–0.3)” +(9)(0.3) (1–0.3)”) = 0.0100 +0.0012 +0.00006 =0.0113