Question

The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour. What are the chances that 3 or 4 customers will arrive in a 15-minute period:

a. Use the binomial distribution
b. Apply the Poisson distribution
c. Employ the normal distribution
d. Use the exponential distribution

Answer 1

To find the chances of 3 or 4 customers arriving in a 15-minute period, we can use the binomial distribution.

Step-by-step explanation:

b. To find the probability that 3 or 4 customers will arrive in a 15-minute period using the binomial distribution, we need to calculate the probability of 3 customers arriving and add it to the probability of 4 customers arriving. The probability of getting exactly 3 customers in a 15-minute period is given by:

P(3 customers) = C(4, 3) * (10/60)^3 * (50/60)^1

Similarly, the probability of getting exactly 4 customers in a 15-minute period is given by:

P(4 customers) = C(4, 4) * (10/60)^4 * (50/60)^0

Finally, we can sum these probabilities to get the total probability:

P(3 or 4 customers) = P(3 customers) + P(4 customers)

Using these equations, you can calculate the probabilities.