THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
70% of the customers at the local ice cream shop order their ice cream on a sugar cone.Assume that the next ten customers order independently of one another.
-What is the probability that more than half of them order sugar cones?
A)0.95
B)0.85
C)0.05
D)0.15

Question

Quizplus · Accepted Answer

Since 70% of the customers order on a sugar cone, we can assume that the probability of each customer ordering on a sugar cone is 0.7. Using the binomial distribution formula, we can find the probability of more than half of the next 10 customers ordering sugar cones:
P(X > 5) = 1 - P(X ≤ 5)
= 1 - (0.7)^0*(0.3)^10 - (0.7)^1*(0.3)^9 - (0.7)^2*(0.3)^8 - (0.7)^3*(0.3)^7 - (0.7)^4*(0.3)^6 - (0.7)^5*(0.3)^5
= 1 - 0.0000001 - 0.000003 - 0.000049 - 0.000456 - 0.002845 - 0.012437
= 0.9842
So the probability of more than half of the next 10 customers ordering sugar cones is 0.9842, which is closest to 0.85 (answer B).