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 at most 3 accidents
Advertisements
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(atmost 3 accident) = P(X ≤ 3)
= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= `[("e"^-4(4)^0)/(0!) + "e"^-4 (4)^1/(1!) + ("e"^-4(4)^2)/(2!) + ("e"^-4(4)^3)/(3!)]`
= `"e"^-4 [4^0/(0!) + 4^1/(1!) + 4^2/(2!) + 4^3/(3!)]`
= `0.0183 [1 + 4 + 16/2 + 64/6]`
= `0.0183 [1 + 4 8 + 32/3]`
= `0.0183[1 + 2/3]`
= `0.0183[(9 + 32)/3]`
= `0.0061[71]`
= 0.4331
Out of 100 days there will be at most 3 acccident = n × P(X ≤ 3)
= 100 × 0.4331
= 43.31
= 43 days ........(approximately)
APPEARS IN
RELATED QUESTIONS
If 5% of the items produced turn out to be defective, then find out the probability that out of 20 items selected at random there are atleast two defectives
Defects in yarn manufactured by a local mill can be approximated by a distribution with a mean of 1.2 defects for every 6 metres of length. If lengths of 6 metres are to be inspected, find the probability of less than 2 defects
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?
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?
The mortality rate for a certain disease is 7 in 1000. What is the probability for just 2 deaths on account of this disease in a group of 400? [Given e–2.8 = 0.06]
Time taken by a construction company to construct a flyover is a normal variate with mean 400 labour days and a standard deviation of 100 labour days. If the company promises to construct the flyover in 450 days or less and agree to pay a penalty of ₹ 10,000 for each labour day spent in excess of 450. What is the probability that the company takes at most 500 days to complete the flyover?
Choose the correct alternative:
Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be:
Choose the correct alternative:
If the area to the left of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?
Vehicles pass through a junction on a busy road at an average rate of 300 per hour. What is the expected number passing in two minutes?
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 less than $40,000?
