Advertisements
Advertisements
Question
The distribution of the number of road accidents per day in a city is poisson with mean 4. Find the number of days out of 100 days when there will be atleast 2 accidents
Solution
In a possion distribution
Mean λ = 4
n = 100
x follows possion distribution with
P(x) = `("e"^(-lambda) lamda^x)/(x!)`
= `("e"^-4 (4)^x)/(x!)`
P(atleast 2 accidents)
= P(X ≥ 2)
= P(X = 2) + P(X = 3) + P(X = 4) + …………
= 1 – P(X < 2)
= 1 – [P(X = 0) + P(X = 1)]
= `1 - [("e"^-4(4)^0)/(0!) + ("e"^-4(4)^1)/(1!)]`
= 1 – e-4[l + 4]
= 1 – 0.0183(5)
= 1 – 0.0915
= 0.9085
= Out of 100 days there will be atleast 2 accidents
= n × P(X ≥ 2)
= 100 × 0.9085
= 90.85
= 91 days .......(approximately)
APPEARS IN
RELATED QUESTIONS
If the probability of success is 0.09, how many trials are needed to have a probability of atleast one success as 1/3 or more?
Among 28 professors of a certain department, 18 drive foreign cars and 10 drive local made cars. If 5 of these professors are selected at random, what is the probability that atleast 3 of them drive foreign cars?
Out of 750 families with 4 children each, how many families would be expected to have atleast one boy
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that 12 of the travelers will not have a laptop?
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that atleast three of the travelers have a laptop?
The average number of customers, who appear in a counter of a certain bank per minute is two. Find the probability that during a given minute three or more customers appear
Choose the correct alternative:
Which of the following cannot generate a Poisson distribution?
Choose the correct alternative:
The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of ₹ 180,000 and a standard deviation of ₹ 10,000. What is the probability that a randomly selected newly qualified CA will earn between ₹ 165,000 and ₹ 175,000?
The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. What percent of people earn between $45,000 and $65,000?
People’s monthly electric bills in Chennai are normally distributed with a mean of ₹ 225 and a standard deviation of ₹ 55. Those people spend a lot of time online. In a group of 500 customers, how many would we expect to have a bill that is ₹ 100 or less?
