Question

32 percent of the customers of a fast food chain order the Whopper, French fries and a drink. A random sample of 10 cash register receipts is selected. What is the probability that eight receipts will show that the above three food items were ordered?

Answer 1

Answer: 0.0023

Explanation:

Let X be the binomial variable that represents the number of receipts will show that the above three food items were ordered.

probability of success p = 32% = 0.32

Sample size : n= 10

Binomial probability function :

`P(X=x)= \ ^nC_xp^x(1-p)^(n-x)`

Now, the probability that eight receipts will show that the above three food items were ordered :

`P(X=8)=\ ^(10)C_8(0.32)^8(1-0.32)^2\\\\=(10!)/(8!2!)(0.32)^8(0.68)^2\\\\=5*9(0.0000508414176684)\\\\=0.00228786379508\approx0.0023`

hence, the required probability = 0.0023