Johnny X owns a gift shop in New York. Last year she evaluated that the probabil

Question

Johnny X owns a gift shop in New York. Last year she evaluated that the probability of a customer who says they are just browsing, buys something, is 30%. Suppose that on a particular day this year 15 customers browse in the store each hour.

Assuming a binomial distribution, respond to the following questions:

Develop the individual probability distribution histogram for all the possible outcomes.

What is the probability that at least one customer, who says they are browsing, will buy something during a specified hour?

What is the probability that at least four customers, who say they are browsing, will buy something during a specified hour?

What is the probability that no customers, who say they are browsing, will buy something during a specified hour?

What is the probability that no more than four customers, who say they are browsing, will buy something during a specified hour?

Explanation / Answer

This follow binomial distribution for Bernouilli trials.

P(X=r)=nCr(p)^r(q)^n-r, where, p is the probbaility of success, n i sthe total number of suceess and r is the number of success in n trials.

P(x>=1)=1-P(x<1)=1-P(x=0)=1-0.005=0.995

P(x>=4)=1-P(x<4)=1-0.297=0.703

P(x=0)=15C0(0.30)^0(0.70)^15=0.005

P(x<=4)=P(x=0)+....+P(x=4)=0.515

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