You are working in the cafeteria of a hospital and notice that 70% of the patien

Question

You are working in the cafeteria of a hospital and notice that 70% of the patients order/ prefer regular soda to diet soda. You decide to conduct an experiment on the next 10 patient orders coming into the cafeteria (Hint…this is a binomial problem) A) what is the probability that only 2 of the next 10 patient will order regular soda? B) What is the probability that 5 of the next 10 patients will order regular soda? C) What is the expected value, variance and standard deviation of your experiment?

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a.
P( X = 2 ) = ( 10 2 ) * ( 0.7^2) * ( 1 - 0.7 )^8
= 0.0014

b.
P( X = 5 ) = ( 10 5 ) * ( 0.7^5) * ( 1 - 0.7 )^5
= 0.1029
c.
Mean ( np ) =10 * 0.7 = 7
Standard Deviation ( npq )= 10*0.7*0.3 = 1.4491

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