Suppose that, on average, the number of car accidents in Hong Kong are
lilyta79jd
Answered question
2021-11-27
i. Determine the probability that at least χ accidents will occur in 12 hour period.
ii. In a two days, if there were 8 car accidents in Hong Kong, what is the probability that 2 accidents have occurred in the first 12 hours of the two days?
Answer & Explanation
breisgaoyz
Beginner2021-11-28Added 14 answers
Step 1
There are two different types of probability distributions: discrete and continuous. Poisson distribution is a discrete probability distribution.
Poisson distribution is deals with the probability of occurring a number of events in a period of time. There are only one parameter for Poisson distribution, that is . The mean and variance of the Poisson distribution is same as .
Step 2
Let X represent the total number of auto accidents in the 24-hour period in location H. It is assumed that six accidents occur every day. Therefore, X follows a Poisson distribution with parameter .
i) If for 24 hours, for 12 hours will be . Therefore, Y denotes a Poisson random variable with . The probability mass function of the Poisson distribution is given below.
indicates the probability that at least x accidents occur in the 12 hour period and it be calculated and it can be calculated in the following way.
So is the required probability.
Step 3
ii) Let X indicates the number of car accidents in place H in 24 hours period. it is given that 6 accidents occurs in 24 hour period. Thus X follows a Poisson distribution with parameter . Thus for 48 hours the will be 12.
P, the Poisson random variable for the number of accidents in the first 12 hours of a day, a week, or a month, shall be denoted. So . That is . Q denotes the number of accidents in the rest 36 hours of 48 hour period. Thus , thus
Given that 8 car accidents are taken place and the probability for happening 2 accidents in the first 12 hour period has to be calculated (2 happened in the first 12 hours and 6 happened in the rest 36 hours).
Therefore,
Hence, 0.31147 is the required probability.
New Questions in High school statistics
Construct all random samples consisting three observations from the given data. Arrange the observations in ascending order without replacement and repetition.
86 89 92 95 98.Read carefully and choose only one option
A statistic is an unbiased estimator of a parameter when (a) the statistic is calculated from a random sample. (b) in a single sample, the value of the statistic is equal to the value of the parameter. (c) in many samples, the values of the statistic are very close to the value of the parameter. (d) in many samples, the values of the statistic are centered at the value of the parameter. (e) in many samples, the distribution of the statistic has a shape that is approximately NormalFind the mean of the following data: 12,10,15,10,16,12,10,15,15,13.
The equation has a positive slope and a negativey-intercept.
1) y=−2x−3
2) y=2−3x
3) y=2+3x
4) y=−2+3xWhat term refers to the standard deviation of the sampling distribution?
Fill in the blanks to make the statement true: .
What percent of is
The first 15 digits of pi are as follows: 3.14159265358979
The frequency distribution table for the digits is as follows:
Which two digits appear for 3 times each?
A) 1, 7
B) 2, 6
C) 5, 9<br<D) 3, 8How to write
What is the simple interest of a loan for $1000 with 5 percent interest after 3 years?
What number is 12% of 45?
The probability that an automobile being filled with gasoline also needs an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and the filter need changing is 0.10. (a) If the oil has to be changed, what is the probability that a new oil filter is needed? (b) If a new oil filter is needed, what is the probability that the oil has to be changed?
The mean of sample A is significantly different than the mean of sample B. Sample A: Sample B: Use a two-tailed -test of independent samples for the above hypothesis and data. What is the -value?
Leasing a car. The price of the car is$45,000. You have $3000 for a down payment. The term of the lease is and the interest rate is 3.5% APR. The buyout on the lease is51% of its purchase price and it is due at the end of the term. What are the monthly lease payments (before tax)?
What is mean and its advantages?
