The sub-questions for this question are:
a) construct a binomial distribution using n=6 and p=0.34
b) graph the binomial distribution using a histogram and describe it's shape
c) what values of the random variable would you consider unusual? Explain your reasoning.
Answer:
a)
P(X=0) =0.0827
P(X=1) = 0.255
P(X=2) = 0.329
P(X=3) = 0.226
P(X=4) = 0.087
P(X=5) = 0.018
P(X=6) = 0.0015
b) graph D
c) x=5 and x=6
Explanation:
a)
Formula for binomial distribution:
nCx(p^x)(q^(n-x))
Number of sample, n = 6
probability of success, p = 0.34
probability of failure, q = 1-p = 0.66
P(X=0) = 6C0(0.34^0)(0.66^6)
= 1*1*0.0827 = 0.0827
P(X=1) = 6C1(0.34^1)(0.66^5)
= 6*0.34*0.1252 = 0.255
P(X=2) = 6C2(0.34^2)(0.66^4)
= 15*0.1156*0.1897 = 0.329
P(X=3) = 6C3(0.34^3)(0.66^3)
= 20*0.0113 = 0.226
P(X=4) = 6C4(0.34^4)(0.66^2)
= 15*0.0058 = 0.087
P(X=5) = 6C5(0.34^5)(0.66^1)
= 6*0.003 = 0.018
P(X=6) = 6C6(0.34^6)(0.66^0)
= 1*0.0015 = 0.0015
b) the shape of the graph is the graph shape. Referring to the attachment, the correct graph is D
c) the unusual values would be x=6 and x=5, because those values are too small and lower than 0.05