A limousine service receives 236 calls over 40 days from customers who need a ride to the airport.Use the Poisson distribution to find the probability that fewer than 2 customers need a ride on a given day.Do not round intermediate computations, and round your answer to three decimal places.(If necessary, consult a list of formulas.)
Question
A limousine service receives 236 calls over 40 days from customers who need a ride to the airport.Use the Poisson distribution to find the probability that fewer than 2 customers need a ride on a given day.Do not round intermediate computations, and round your answer to three decimal places.(If necessary, consult a list of formulas.)
Solution
To solve this problem, we first need to find the average number of calls per day.
Step 1: Find the average number of calls per day The limousine service receives 236 calls over 40 days. So, the average number of calls per day (λ) is 236/40 = 5.9 calls per day.
Step 2: Use the Poisson distribution formula The Poisson distribution formula is P(x; λ) = (e^-λ * λ^x) / x!, where:
- P(x; λ) is the probability of x events in an interval,
- e is the base of the natural logarithm (approximately equal to 2.71828),
- λ is the average rate of value,
- x is the actual number of successes that result from the experiment, and
- x! is the factorial of x.
We want to find the probability that fewer than 2 customers need a ride on a given day. This means we need to find P(0; 5.9) + P(1; 5.9).
Step 3: Calculate P(0; 5.9) P(0; 5.9) = (e^-5.9 * 5.9^0) / 0! = 0.00277
Step 4: Calculate P(1; 5.9) P(1; 5.9) = (e^-5.9 * 5.9^1) / 1! = 0.01635
Step 5: Add the probabilities P(x < 2) = P(0; 5.9) + P(1; 5.9) = 0.00277 + 0.01635 = 0.01912
So, the probability that fewer than 2 customers need a ride on a given day is 0.019, or 1.9% when rounded to three decimal places.
Similar Questions
A taxi service receives 378 calls over 35 days from customers who need a ride to the airport.Use the Poisson distribution to find the probability that exactly 9 customers need a ride on a given day.Do not round intermediate computations, and round your answer to three decimal places.(If necessary, consult a list of formulas.)
A service station owner in a country town has an average of 6 cars per hour arriving for petrol. Assuming a Poisson distribution, find the probability that 3 cars refuel in a 15 minute period.
The food court at an amusement park has an ice cream shop. The shop has 17 customers arrive over 85 minutes.Use the Poisson distribution to find the probability that the shop has more than 1 arrival in a given minute.Do not round intermediate computations, and round your answer to three decimal places.(If necessary, consult a list of formulas.)
A car-hire firm has two cars, which it hires out day by day. The number of demand for a car on each day follows Poissondistribution with mean 1.5. Calculate the proportion of days on which neither car is used
A park receives an average of 20 tourists per hour. Assuming that the arrival time of tourists follows a Poisson distribution, what is the probability that exactly 8 tourists will be received in any given hour?Round your results to four decimal places.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.