Statistics
posted by Kayse .
I have a problem I need some help on. I have answered parts. Any guidance would be appreciated. K
For many years the numbers of accidents per week at a hazardous intersection have been studied. The number of accidents per week varies with mean 2.2 and standard deveiation 1.4.
1. Could the exact distributin of the number of accidents per week be described by a normal distribution?
I've drawn the normal curve showing the mean of 2.2 in the center of the curve and deviating both directions 1.4
2. Looking at only 52 weeks we can calculate xbar the mean number of accidents per week. What is the approximate distribution of xbar according to the Central Limit Theorem?
N(2.2, 0.194)
3. What is the approximate probability that xbar is greater than 2 accidents per week?
P(xbar > 2)
4. What is the probability that there are fewer than 100 accidents at the intersection in a year?
1. Could the exact distribution of the number of accidents per week be described by a normal distribution?
No, because the number of accidents is always an integer larger or equal than zero.
But the mean number of accidents per week, computed over some time T does tend to the normal distribution for
T > infinity. The standard deviation of the mean over a period of T is the original standard deviation divided by sqrt(T).
Thanks, what about probability that there are fewer than 100 accidents at the intersection in a year? The hint says to "restate the event in terms of xbar minus mean number of accidents per week.
If you have 100 accidents in a given year, then in that year the average per week was xbar = 100/52. You know what the true average is and you know what the standard deviation of the yearly average is (sigma/sqrt[52]).
You then look up the probability that
Z < (xbar  average)/[sigma/sqrt[52]]
from the standard normal distribution table, or using statistical software.
Respond to this Question
Similar Questions

Algebra story problem
I need to turn this story into an algebra problem: Your cousin ears $25 per week babysitting and receives one $5 bonus. You earn $15 per week mowing lawns and $12 a week running errands. After working the same number of weeks, you … 
Statistics
I have a problem I need some help on. I answered some. For many years the numbers of accidents per week at a hazardous intersection have been studied. The number of accidents per week varies with mean 2.2 and standard deveiation 1.4. … 
Calculus
At the moment OHaganBooks is selling 1000 books per week and its sales are rising at a rate of 200 books per week. Also, it is now selling all its books for $20 each, but the price is dropping at a rate of $1 per week. I need to know … 
Calculus
At the moment OHaganBooks is selling 1000 books per week and its sales are rising at a rate of 200 books per week. Also, it is now selling all its books for $20 each, but the price is dropping at a rate of $1 per week. I need to know … 
Calculus
At the moment OHaganBooks is selling 1000 books per week and its sales are rising at a rate of 200 books per week. Also, it is now selling all its books for $20 each, but the price is dropping at a rate of $1 per week. I need to know … 
Statistics
For the past week I have been trying to find Canadian statistics for the drug Clomid. I can't find anything, and I really need some sort of statistical data, either just numbers or a graph...can anyone find this and tell me where it … 
Math Statistics
An investigational drug study is being conducted. The initial screening phase needs to include enough people so that the final (approved) group has at least 10 patients. The probability of a person being approved for the study is .80. … 
Statistics
2.) Car insurance companies assume that the longer a person has been driving, the less likely they will be in an accident, and therefore charge new drivers higher insurance premiums than experienced drivers. To determine whether driving … 
statistics
The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. a. What is the distribution of Xbar, the mean number of accidents in one year, (52 weeks)? 
Statistics
Before i state my question I would like to note that I have to do a one tailed test but i don't know how to with the information given. I need a standard deviation, i need a mean, but do i use the mean for yrs drivin or number accidents. …