Question

# Assume that X is a binomial random variable with n = 15 and p = 0.78....

Assume that X is a binomial random variable with n = 15 and p = 0.78. Calculate the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

Assume that X is a binomial random variable with n = 15 and p = 0.78. Calculate the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

 a. P(X = 14) b. P(X = 13) c. P(X ≥ 13)

Solution

Given that ,

p = 0.78

1 - p = 1 - 0.78 = 0.22

n = 15

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x

a)

x = 14

P(X = 14) = ((15! / 14! (1)!) * 0.7814 * (0.22)1

= 0.1018

Probability = 0.1018

b)

x = 13

P(X = 13) = ((15! / 13! (2)!) * 0.7813 * (0.22)2

= 0.2010

Probability = 0.2010

b)

P(X 13) = P(X = 13) + P(X = 14) + P(X = 15)

=  ((15! / 13! (2)!) * 0.7813 * (0.22)2 + ((15! / 14! (1)!) * 0.7814 * (0.22)1 + ((15! / 15! (0)!) * 0.7815 * (0.22)0

= 0.3269

Probability = 0.3269

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