SOLUTION: On average there are three babies born a day at the Hospital with hair on their backs. Find the probability that in one day no babies are born with hair on their backs.

Question 1168310: On average there are three babies born a day at the Hospital with hair on their backs. Find the probability that in one day no babies are born with hair on their backs.

Round answer to 4 decimal places.
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
This problem can be solved using the Poisson distribution, which is used to model the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known average rate and independently of the time since the last event.
**1. Understand the Poisson Distribution**
* The Poisson distribution formula is: P(X = k) = (e^(-λ) * λ^k) / k!
* P(X = k) is the probability of k events occurring.
* λ (lambda) is the average number of events (in this case, babies born with hair on their backs).
* e is Euler's number (approximately 2.71828).
* k! is the factorial of k.
**2. Identify the Values**
* λ = 3 (average number of babies born with hair on their backs per day)
* k = 0 (we want to find the probability of no babies born with hair on their backs)
**3. Apply the Poisson Formula**
* P(X = 0) = (e^(-3) * 3^0) / 0!
* P(X = 0) = (e^(-3) * 1) / 1
* P(X = 0) = e^(-3)
**4. Calculate the Probability**
* e^(-3) ≈ 0.049787
**5. Round to 4 Decimal Places**
* P(X = 0) ≈ 0.0498
**Therefore, the probability that no babies are born with hair on their backs in one day is approximately 0.0498.**

RELATED QUESTIONS
Ignoring twins and other multiple births, assume babies born at a hospital are... (answered by stanbon)

One day, eleven babies are born at a hospital. Assuming each baby has an equal chance of... (answered by mathmate)

One day 13 babies are born at a hospital. Assuming each baby has an equal chance of being (answered by Boreal,ikleyn)

Suppose the number of babies born each hour at a hospital follows a Poisson distribution... (answered by Boreal)

a mean of 210.0 case of low birth weight each year. 1. Find the mean number of low... (answered by robertb)

The average weight of all newborn babies at Dearborn Hospital was estimated by using the... (answered by ewatrrr)

25 babies are born in a hospital in a week. Find the probability that a) At least 12... (answered by Boreal)

The maternity ward at Dr. Jose Fabella Memorial Hospital in Manila in the Philippines is... (answered by Boreal)

Suppose that of all babies born in a particular hospital are girls. If babies born in... (answered by Fombitz)