A popular doughnut shop makes 5000 doughnuts per day, of which 30% (1500 doughnu

Question

A popular doughnut shop makes 5000 doughnuts per day, of which 30% (1500 doughnuts) have chocolate icing. Andy likes doughnuts with chocolate icing but his brother Jimmy tells the shop assistant to choose doughnuts randomly whenever he buys them.

A-Every Sunday, Jimmy buys 15 doughnuts and brings them home. On average, how many of these doughnuts will have chocolate icing?

B-determine the probability that on a given Sunday, there will be at least 6 doughnuts with chocolate icing that Jimmy has brought home.

c-n a month of 4 Sundays, what is the probability that Jimmy from will not bring home at least 6 doughnuts with chocolate icing on any of the Sundays.

Explanation / Answer

p = .30, n = 15

1) 15*.30 = 4.5( ~ 5)doughnuts, On an average, will have chocolate icing

2) Using TI (highly recommended for cumulative probabilities)

p(x >= 6) = 1 - binomcdf(15, .30, 5)

p(x >= 6) = .2784 (also, highly recommended for cumulative probabilities)

3) (1- P(x>=6))^4 = 0.2711

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