Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Out of 750 families with 4 children each, how many families would be expected to have atmost 2 girls
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:
Which of the following cannot generate a Poisson distribution?
Choose the correct alternative:
The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84?
Choose the correct alternative:
Using the standard normal table, the sum of the probabilities to the right of z = 2.18 and to the left of z = – 1.75 is
Choose the correct alternative:
Monthly expenditure on their credit cards, by credit cardholders from a certain bank, follows a normal distribution with a mean of ₹ 1,295.00 and a standard deviation of ₹ 750.00. What proportion of credit cardholders spend more than ₹ 1,500.00 on their credit cards per month?
Vehicles pass through a junction on a busy road at an average rate of 300 per hour. Find the probability that none passes in a given minute
Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Raghul wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Raghul takes the test and scores 585. Will he be admitted to this university?
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?
