Question

Compute the following binomial probabilities directly from the formula for b(x|n,p): b(3|8, .35) b(5|8, .6) P(3 ≤ X ≤ 5) when n=7 and p=.6 P(1 ≤ X) when n=9 and p=.1

Answer 1

Explanation:

From the information given,

p represents the probability of success.

x represents the number of success

n represents the number of samples

Therefore,

1) b(x|n,p): b(3|8, .35)

x = 3

n = 8

p = 0.35

From the binomial probability distribution calculator,

P(x = 3) = 0.28

1) b(x|n,p): b(5|8, .6)

x = 5

n = 8

p = 0.6

From the binomial probability distribution calculator,

P(x = 5) = 0.28

c) n = 7

p = 0.6

P(3 ≤ X ≤ 5)

P(x ≥ 3) = 0.904

P(x ≤ 5) = 0.841

P(3 ≤ X ≤ 5) = 0.904 - 0.841 = 0.063

d) n = 9

p = 0.1

P(1 ≤ X) = p(x ≥ 1)

p(x ≥ 1) = 0.61