Question

The average number of babies born at a hospital is 6 per hour. What is the probability that three babies are born during a particular 1 hour period?

249

likes
1244 views

Answer to a math question The average number of babies born at a hospital is 6 per hour. What is the probability that three babies are born during a particular 1 hour period?

Expert avatar
Jon
4.6
108 Answers
To solve this problem, we can use the Poisson distribution. The Poisson distribution is commonly used when we want to calculate the probability of a certain number of events occurring within a specific time period, given the average rate of occurrence.

The Poisson distribution is defined as:

P(X = k) = \frac{\lambda^k \cdot e^{-\lambda}}{k!}

where:
- P(X = k) is the probability of k events occurring
- \lambda is the average rate of events occurring in the given time period
- e is the base of the natural logarithm
- k! is the factorial of k, which represents the number of ways to arrange k events

In this problem, the average rate of babies born per hour is 6 ( \lambda = 6 ) and we want to find the probability of three babies being born in a particular 1-hour period ( k = 3 ).

Using the Poisson distribution formula, we can calculate the probability:

P(X = 3) = \frac{6^3 \cdot e^{-6}}{3!}

Simplifying further:

P(X = 3) = \frac{216 \cdot e^{-6}}{6}

Calculating the value of e^{-6} :

e^{-6} \approx 0.00248

Substituting this value into the probability formula:

P(X = 3) = \frac{216 \cdot 0.00248}{6}

Simplifying further:

P(X = 3) \approx 0.089

Therefore, the probability that three babies are born during a particular 1-hour period is approximately 0.089.

Answer: \approx 0.089

Frequently asked questions (FAQs)
What is the sine of an angle θ if the tangent of θ is -0.75?
+
What is the sine ratio of an acute angle if the opposite side is 3 units and the hypotenuse is 5 units?
+
What is the result of applying the function f(x) = 2x + 5 to the input x = 10?
+
New questions in Mathematics
1 + 1
Use the elimination to find the solution to each linear system. X+y=43 2x-y=20
Suppose a large shipment of cell phones contain 21% defective. If the sample of size 204 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 4% round your answer to four decimal places
Let f(x) = x² − 1. Find the equation of the tangent line to the graph of f at the point x0 = 2.
A company that manufactures personal hygiene items purchases machinery for $220,000 that is considered to last 7 years; it is estimated that at the end of the period it will have a salvage value of $1000. Find: to. The depreciation rate. b. The book value at the end of the sixth year.
Reparameterize the curve r(t)= cos(t)i without (t)j (t)k by the arc length.
4x/2+5x-3/6=7/8-1/4-x
Solve : 15/16 divide 12/8 =x/y
The market for economics textbooks is represented by the following supply and demand equations: P = 5 + 2Qs P = 20 - Qd Where P is the price in £s and Qs and Qd are the quantities supplied and demanded in thousands. What is the equilibrium price?
Shows two blocks, masses 4.3 kg and 5.4 kg, being pushed across a frictionless surface by a 22.5-N horizontal force applied to the 4.3-kg block. A. What is the acceleration of the blocks? B. What is the force of the 4.3-kg block on the 5.4 -kg block? C. What is the force of the 5.4 -kg block on the 4.3 -kg block?
X³-27
Congratulations, you have saved well and are ready to begin your retirement. If you have $1,750,000.00 saved for your retirement and want it to last for 40 years, and will earn 10.8% compounded monthly: What is the amount of the monthly distribuion? 216.50 How much interest is earned in retirement?
7.57 Online communication. A study suggests that the average college student spends 10 hours per week communicating with others online. You believe that this is an underestimate and decide to collect your own sample for a hypothesis test. You randomly sample 60 students from your dorm and find that on average they spent 13.5 hours a week communicating with others online. A friend of yours, who offers to help you with the hypothesis test, comes up with the following set of hypotheses. Indicate any errors you see. H0 :x ̄<10hours HA : x ̄ > 13.5 hours
A person runs 175 yards per minute write a variable that represents the relationship between time and distance
Let N be the total number of ways to choose at least one ride, out of a total of 7 different ones, existing in an amusement park. Can it be said that N is a natural number equal to?
a) 6x − 5 > x + 20
simplify w+[6+(-5)]
How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7
calculate the product of 4 and 1/8
The length of a rectangle is five more than its width. if the perimeter is 120, find both the length and the width.