Question

At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .56. a. Find the probability that in a sample of 15 customers, none of the 15 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.) Probability b. Find the probability that in a sample of 15 customers, at least 4 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.) Probability c. Find the probability that in a sample of 15 customers, fewer than 5 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.) Probability d. Find the probability that in a sample of 15 customers, all 15 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.) Probability

Answer 1

Answer:

a. 0.0000

b. 0.9949

c. 0.0212

d. 1.0000

Step-by-step explanation:

a. This is a binomial probability distribution problem of the form:

$P(X=x)={n\choose x}p^x(1-p)^{n-x}$

#Given n=15, p=0.56, the probability of none will order a non-alcoholic drink:

$P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\\\P(X=0)={15\choose 0}0.56^0(1-0.56)^{15}\\\\\\=0.0000045$

$\approx 0.0000$

Hence, the probability that none will order a non-alcoholic drink is 0.0000

b. The probability that at least 4 will order a non-alcoholic drink is:

$P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X\geq 4)=1-P(X$

Hence, the probability of at least 4 non-alcoholic orders is 0.9949

c. The Probability that fewer than 5 orders will be made is calculated as:

$P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X$

Hence, the probability of less than 5 orders is 0.0212

d. The probability of all orders being non-alcoholic is equivalent to 1  minus no order being non-alcoholic.

-From a above, the probability of zero non-alcoholic order is , P(X=0)=0000045

-Therefore:

$P(All)=1-P(none)\\\\=1-0.0000045\\\\=0.999996$

$\approx 1.0000$

Hence, the probability that all orders are non-alcoholic 1.0000