If x is a binomial random variable, use the binomial probability table to find t

Question

If x is a binomial random variable, use the binomial probability table to find the probabilities belowa. P(x=3) for n=10, p=0.6

b. P(x4) for n=15, p=0.3

c. P(x>1) for n=5, p=0.1

d. P(x<9) for n=20, p=0.8

e. P(x8) for n=25, p=0.6

f. P(x=3) for n=20, p=0.4

a. P(x=3)=

(Round to three decimal places as needed.)

b. P(x4)=

(Round to three decimal places as needed.)

c. P(x>1)=

(Round to three decimal places as needed.)

d. P(x<9)=

(Round to three decimal places as needed.)

e. P(x8)=

(Round to three decimal places as needed.)

f. P(x=3)=

(Round to three decimal places as needed.)

Explanation / Answer

Solution:-

a) P(x = 3) = 0.042

P(x = 3) for n = 10, p = 0.6

By applying binomial distribution:-

P(x, n, p) = nCx*px * (1-p) (n-x)

P(x = 3) = 0.042467

b. P(x 4) = 0.515

P(x 4) for n =15, p = 0.3

P(x 4) = 0.51549

c. P(x > 1) = 0.081

P(x > 1) for n = 5, p = 0.1

P(x > 1) = 0.08146

d. P(x < 9) = 0

P(x < 9) for n = 20, p = 0.8

P(x < 9) = 0.000101

e. P(x 8) = 0.999

P(x 8) for n = 25, p = 0.6

P(x 8) = 0.99879

f. P(x = 3) = 0.012

P(x = 3) for n = 20, p = 0.4

P(x = 3) = 0.012349

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