In a binomial distribution, n = 12 and π = .60. a. find the probability for x = 5? (round your answer to 3 decimal places.) probability b. find the probability for x ≤ 5? (round your answer to 3 decimal places.) probability c. find the probability for x ≥ 6?

For binomial distribute we use formula

the probability mass function of the binomial distribution is:

Given n = 12 and π = .6. (Replace the values)

the probability for x = 5, we need to find P(x=5). Here r= 5

P(x=5)=

= = 0.10090 = 0.101

(b) the probability for x ≤ 5

P(x<=5) = P(x=0) + P(x=1) +P(x=2)+ P(x=3) + P(x=4) + P(x=5)

P(x<=5) = + +   + + +

= 0.15821229 = 0.158

(c) find the probability for x ≥ 6

P(x>=6) =P(x=6) + P(x=7) +P(x=8)+ P(x=9) + P(x=10) + P(x=11)+ P(x=12)

P(x>=6) = + + + + +    +  

= 0.8417877 = 0.0842 (rounded to 3 decimal places)

a= 0.101 b= 0.158 c= 0.842

Step-by-step explanation: using the formula: nCr (pi)^r (1-pi)^n-r

a

step-by-step explanation: