Need help w/a Math Question (stats)

Test Preparation AP Test Preparation
1

<p>A summer resort rents rowboats to customers but does not allow more than
four people to a boat. Each boat is designed to hold no more than 800 pounds.
Suppose the distribution of adult males who rent boats, including their clothes
and gear, is normal with a mean of 190 pounds and standard deviation of 10
pounds. If the weights of individual passengers are independent, what is the
probability that a group of four adult male passengers will exceed the acceptable
weight limit of 800 pounds?
(A) 0.023
(B) 0.046
(C) 0.159
(D) 0.317
(E) 0.977</p>

<p>I know that the answer is A...but I don't know how to solve to get that answer. can anyone help me?</p>

2

<p>There are a few ways...You can either divide 800 by four or multiply 190 by 4.</p>

<p>So 190 x 4 = 760</p>

<p>New SD is 10 squared x 4 (people) and sqrt all that down to 20 </p>

<p>Draw yourself a normal model. Whats the P(the combined weights are at least 800 or above) This is an upper tail test.</p>

<p>So you find your z score (if it weren't normal than a t-score for means). </p>

<p>800-760/20 = 2</p>

<p>On your calc... under 2nd vars.....normcdf(2,9^9)</p>

<p>Which gives you .02275 rounded to .023 and thats A for you.</p>

3

<p>I’m confused about this same question. SD-squared gives you the variance of one person, or one random variable, but then don’t you need to multiply the variance by the number of random variables squared? And square root that total variance?</p>

4

<p>I don’t see why it’s not a standard dev. of 40, with 800 having a z-score of 1, and why and the answer isnt C. Could someone explain?</p>

5

<p>The variance of one person is 100. Therefore, the variance of 4 people is 400, and the square root of that is 20. How’d you get 40?</p>

6

<p>That’s strange. Our stat book has different rules for variances. For example, if the variance of a random variable X is 100, the variance of bX is b-squared variance X.</p>

<p>Therefore, in the problem, if the variance of one person (X) is 100, the variance of four people is 16 times variance of X, or 1600. And the square root of that is 40. Haha, idk, that’s how we learned it? I’m a little concerned now.</p>

7

<p>That’s not a different rule. If the variance of X is 100, then the variance of bX is, in fact, b^2 times the variance of X.</p>

<p>The thing is, 4X is not the random variable in the problem; that would be the weight of one person, multiplied by four. What you’re doing in the problem is adding together four random variables, each of which has the same distribution as the weight of one person. So you have to use the rules for adding random variables, not multiplying them by a constant.</p>

8

<p>Wow. That makes a ridiculous amount of sense. I don’t know why we’ve been incorrectly using that rule in my stat class. Thank you so much!</p>