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 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random none will be defective
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 children of both sexes? Assume equal probabilities for boys and girls.
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes
Derive the mean and variance of poisson distribution
Define Standard normal variate
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:
In a large statistics class, the heights of the students are normally distributed with a mean of 172 cm and a variance of 25 cm. What proportion of students is between 165cm and 181 cm in height?
The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time. Between 20 and 22 hours?
X is a normally distributed variable with mean µ = 30 and standard deviation σ = 4. Find P(30 < X < 35)
