Assume a binomial probability distribution with n =

Answered question

2022-03-25

Assume a binomial probability distribution with n = 50 and p =0.25. Compute the following: a. The mean and standard deviation of the random variable. b. The probability that X is 15 or more. c. The probability that X is 10 or less.

Answer & Explanation

alenahelenash

alenahelenash

Expert2022-03-28Added 556 answers

GIven thnat the random vanable X follows a binomial distribution with n= 50 and π=0.25

a) Mean of the random variable

μ=nπ

=50×0.25

=12.5

Standard deviation of the randeom variable

σ=nπ(1-π)

=50×0.25×(1-0.25)

=50×0.25×0.75

=9.375

σ=3.0619

b) Apply the correction factor to find the probability of X is 15 or more is nothing but the area above 14.5, that is,

P(x14.5)=P(x-μσ14.5-12.53.0619)

=P(z0.65)

=1-P(z0.65)

=1-(=NORMDIST(0.65)) [Using the Excel function]

=1-0.7422

P(x14.5)=0.2578

Therefore, the reauired probability is 0.2578

c) Apply the correction factor to find the probability of X is 10 or less is nothing but the area below 10.5, that is,

P(x10.5)=P(x-μσ10.5-12.53.0619)

=P(z-0.65)

=(=NORMDIST(-0.65)) [Using the Excel function]

P(x10.5)=0.2578

Therefore, the reauired probability is 0.2578

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