The number of monthly accidents happening in a certain...

The number of monthly accidents happening in a certain street is lognormally distributed with mean \(\mu = 3.7\) and standard deviation \(\sigma = 1\). What is the probability that the number of monthly accidents will be between 29 and 52? A. 0.09 ?. 0.15 C. 0.228 D. 0.356 ?. 0.469 F. 0.596 G. 0.718 Note: copying answers from chegg, using chat GPT, fake and wrong answers will be directly downvoted. Good answers will get an upvote. Please don't answer if you're not sure.

Transcript

00:01 So this table contains the probability distribution for the number of traffic accidents daily in a small town.

00:07 So x is the number of traffic accidents in a small town.

00:18 And this is the probability of 0 is 0 .34, probability of 1 is 0 .27, and so on and so forth.

00:25 And so what we're going to do is, given this distribution, we want to, a, we want to find the mean number of accidents.

00:32 So the mean is the expected value of x.

00:37 And we find that by taking the sum of the x values multiplied by their respective probabilities.

00:43 So x times p of x, and add all those up.

00:46 The next part, and i'm going to do this kind of at the same time because it's very much connected to the mean.

00:52 We want to find the standard deviation, sigma.

00:56 And sigma is found by taking the square root of the variance of x.

01:05 Well, what's the variance of x? so the variance of x is found by taking the expected value of x squared minus the expected value of x quantity squared.

01:19 And this we'll know, right? and that's why i'm saying that a and b are related, because we need the mean of expected value of x to square that quantity for the variance.

01:29 The only other piece that we need to explain here is this expected value of x squared.

01:32 This is found by taking the sum of all the x values squared.

01:39 So 0 squared, 1 squared, 2 squared.

01:41 And then taking that squared value and multiplying it by the probability of x.

01:45 So now we're just doing a bunch of multiplying and adding, and then we're good to go.

01:51 So here we go.

01:52 Let's do it.

01:53 So the mean first.

01:54 Well, actually, before we do that, just to make sure you've entered your probabilities incorrect.

01:58 They should all sum to 1 for it to be a distribution.

02:01 I've seen it where students will misplace, say, the 0 .37 with something like 0 .73, right? and then you get a different value at the end.

02:09 So just make sure your probabilities all sum to 1.

02:12 So just be aware of that.

02:13 And they do.

02:14 So here we go.

02:15 Here, this column is the x times p of x values.

02:18 0 times 0 .34 is 0.

02:20 1 times 0 .27 is 0 .37.

02:22 2 times 0 .13 is 0 .26, and so on and so forth.

02:24 Add them up.

02:25 And this, my friends, is our mean, 1 .23.

02:30 Which we can put into our formula here, right? 1 .23 squared.

02:40 So now we need the expected value of x squared...

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