Question

At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .33.

a. Find the probability that in a sample of 8 customers, none of the 8 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.)
  
Probability:   

b. Find the probability that in a sample of 8 customers, at least 5 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.)
  
Probability:

Find the probability that in a sample of 8 customers, fewer than 7 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.)

Probability:

Answer 1

P(ordering a nonalcoholic beverage), p = 0.33

q = 1 - 0.33 = 0.67

Sample size, n = 8

Binomial distribution: P(X) = nCx p^x q^n-x

a. P(none of the 8 will order a nonalcoholic beverage) = P(0)

= 0.67⁸

= 0.0406

b. P(at least 5 will order a nonalcoholic beverage) = P(X 5)

= P(5) + P(6) + P(7) + P(8)

= 8C5x0.33⁵x0.67³ + 8C6x0.33⁶x0.67² + 8C7x0.33⁷x0.67 + 0.33⁸

= 0.0659 + 0.0162 + 0.0023 + 0.0001

= 0.0845

c. P(fewer than 7 will order a nonalcoholic beverage) = P(X < 7)

= 1 - [P(7) + P(8)]

= 1 - (0.0023 + 0.0001)

= 0.9976