Question

In a 24 hours period, the average number of boats arriving at a port is 10. Assuming that boats arrive at a random rate that is the same for all subintervals of equal length (i.e. the probability of a boat arriving during a 1 hour period the same for every 1 hour period no matter what). Calculate the probability that more than 1 boat will arrive during a 1 hour period. (P(X>1) ) Give your answers to 4 decimal places and in a range between 0 and 1

207

likes
1036 views

Answer to a math question In a 24 hours period, the average number of boats arriving at a port is 10. Assuming that boats arrive at a random rate that is the same for all subintervals of equal length (i.e. the probability of a boat arriving during a 1 hour period the same for every 1 hour period no matter what). Calculate the probability that more than 1 boat will arrive during a 1 hour period. (P(X>1) ) Give your answers to 4 decimal places and in a range between 0 and 1

Expert avatar
Fred
4.4
113 Answers
To solve this problem, we will use the Poisson distribution since we are dealing with the arrival of boats over a given time period.

The average number of boats arriving at the port in a 1-hour period is given as 10. Therefore, the average rate parameter, Ξ», is also 10.

The probability of more than 1 boat arriving during a 1-hour period can be calculated as:

P(X > 1) = 1 - P(X = 0) - P(X = 1)

where P(X = k) represents the probability of k boats arriving during a 1-hour period.

Using the formula for the Poisson distribution:

P(X = k) = (e^(-Ξ») * Ξ»^k) / k!

we can calculate each term.

P(X = 0) = (e^(-10) * 10^0) / 0! = e^(-10)

P(X = 1) = (e^(-10) * 10^1) / 1! = 10 * e^(-10)

Now we can substitute these values into the formula for P(X > 1):

P(X > 1) = 1 - e^(-10) - 10 * e^(-10)

Calculating this expression, we find:

P(X > 1) β‰ˆ 1 - e^(-10) - 10 * e^(-10) β‰ˆ 1 - 0.00004540 - 0.00045399 β‰ˆ 0.9995

Therefore, the probability that more than 1 boat will arrive during a 1-hour period is approximately 0.9995.

\textbf{Answer: } P(X > 1) \approx 0.9995

Frequently asked questions (FAQs)
How many different ways can you arrange 5 people in a row for a photograph?
+
Question: What is the area of an equilateral triangle with side length 8?
+
What is the range of the data set: 12, 8, 15, 6, 9, 12, 8, 20, 11, 14?
+
New questions in Mathematics
Students Ana Beatriz and Paula decided to register on a website with exercises to study for upcoming simulations, but to register on this website, they need to choose a password consisting of five characters, three numbers and two letters (capital letters). or lowercase). Letters and numbers can be in any position. They know that the alphabet is made up of twenty-six letters and that an uppercase letter differs from a lowercase letter in a password. What is the total number of possible passwords for registering on this site?
5 . {2/5 + [ (8/-9) - (1/-7) + (-2/5) ] Γ· (2/-5)} . 8/15
Determine all solutions to the inequality |2x + 6| βˆ’ |x + 1| < 6. Write your final answer in interval notation
A consulting company charges a fee of $50 per hour for consulting. If their monthly fixed costs are $1,000 and they want to make a monthly profit of $2,500, how many consulting hours should they bill per month?
The bus one way of the road which is 10km is heading with speed of 20km/h ,then the bus the other 10km is heading with speed of 60km/h. The middle speed of the road is it equal with arithmetic speed of the v1 and v2 ?
The beta of a company is 1,41 and its cost of equity 18,95%. What is then the market risk premium if the risk free rate is 0,94%? (in %, 2 decimal places)
is the x element (180,270), if tanx-3cotx=2, sinx ?
(5y 9)-(y 7)
5.- From the probabilities: 𝐏(𝐁) = πŸ‘πŸŽ% 𝐏(𝐀 ∩ 𝐁) = 𝟐𝟎% 𝐏(𝐀 Μ…) = πŸ•πŸŽ% You are asked to calculate: 𝐏(𝐀 βˆͺ 𝐁)
Solve the equation: sin(2x) = 0.35 Where 0Β° ≀ x ≀ 360Β°. Give your answers to 1 d.p.
Solve equations by equalization method X-8=-2y 2x+y=7
On+January+10+2023+the+CONSTRUCTORA+DEL+ORIENTE+SAC+company+acquires+land+to+develop+a+real estate+project%2C+which+prev%C3% A9+enable+50+lots+for+commercial+use+valued+in+S%2F+50%2C000.00+each+one%2C+the+company+has+as+a+business+model+generate+ cash+flow+through%C3%A9s+of+the+rental%2C+so+47%2C+of+the+50+enabled+lots+are+planned to lease+47%2C+and+ the+rest+will be%C3%A1n+used+by+the+company+for+management%C3%B3n+and+land+control
We have received our p&l statement back from accounts. The board has asked for an innovation hub. What items should we prioritise reviewing to decide if we can afford an innovation hub?
List the remaining zeros of the polynomial with the given zeros Zeros are: 2, 3i, and 3 + i
Find the area of a triangle ABC when m<C = 14 degrees, a = 5.7 miles, and b = 9.3 miles.
Associate each 2nd degree equation with its respective roots. A) x2+6x+8=0 B)x2-5x-6=0
A person runs 175 yards per minute write a variable that represents the relationship between time and distance
Find the vertex F(x)=x^2-10x
23,456 + 3,451
Find the rule that connects the first number to the second number of each pair. Apply the rule to find the missing number in the third pair. (18 is to 22) (54 is to 26) (9 is to ?)