Question

A dentist knows from past records that 10% of customers arrive late for their appointment A new manager believes that there has been a change in the proportion of customers who arrive late for their appointment. A random sample of 50 of the dentist's customers is taken.

(a) Calculate the probability that no more than 8 customers arrive late for their appointment
(b) Calculate the probability that exactly 6 customers arrive late for their appointment.

Answer 1

To calculate the probabilities, we can use the binomial probability formula. For part (a), the probability that no more than 8 customers arrive late is 0.0907. For part (b), the probability that exactly 6 customers arrive late is 0.1625.

Step-by-step explanation:

To solve this problem, we can use the binomial probability formula. In this case, the probability of a customer arriving late is 10% or 0.1. We have a random sample of 50 customers, so we can use the binomial probability formula to calculate the probabilities. Here are the step-by-step calculations for each part:

(a) Probability that no more than 8 customers arrive late

P(X <= 8) = C(50, 0) * (0.1)^0 * (1 - 0.1)^(50 - 0) + C(50, 1) * (0.1)^1 * (1 - 0.1)^(50 - 1) + ... + C(50, 8) * (0.1)^8 * (1 - 0.1)^(50 - 8)

P(X <= 8) = 0.0907

(b) Probability that exactly 6 customers arrive late

P(X = 6) = C(50, 6) * (0.1)^6 * (1 - 0.1)^(50 - 6)

P(X = 6) = 0.1625