Someone wanna a question from a previous AP Stats mc test for me?

Test Preparation AP Test Preparation
1

<p>I'm not sure if this is 1997 or 2002 but this is number 10.</p>

<p>The lengths of individual shellfish in a population of 10,000 selfish are approximately normally distributed with mean 10 centimeters and standard deviation 0.2 centimeter. Which of the following is the shortest interval that contains approximately 4,000 shellfish lengths?</p>

<p>I know the answer is 9.895 - 10.105 cm but I don't quite understand how to approach it.</p>

2

<p>Yep, it’s 2002 MC.</p>

<p>My teacher went over this last week. He used a t-int to tackle this one. o3O</p>

<p>mean +/- t*(STD DEV)
10 +/- .5244(.2)</p>

<p>Does that make sense…?</p>

3

<p>Yeah, that makes sense except how would you find that t value from the chart?</p>

4

<p>how did you get the critical value t*</p>

5

<p>… I don’t even know. That number was just on my paper. </p>

<p>FANTASTIC.</p>

6

<p>yeah I understand what you did except I don’t quite get how you got the t* either lol</p>

7

<p>Okay, I also found invT(.7, 3999) written down as well. Except I don’t understand it either. :(</p>

<p>Sorry folks.</p>

8

<p>In a normal distribution, the shortest interval with any number of items will be in the center because most values fall in the center. So the 4000 fish needed are the middle .4 of the normal curve, so there is .3 before it, and .3 after it. </p>

<p>invNorm(.3)=-.5244
-.5244(.2)+10=9.895</p>

<p>invNorm(.7)=.5244
.5244(.2)+10=10.105</p>

9

<p>I’m not in stats but our teacher taught us some stats in math class let me try to approach this.</p>

<p>4/10 = 0.4
0.4/2 + 0.5 = 0.7</p>

<p>invnorm (0.7) = z-score
now obviously invnorm (0.3) because that way you get 40% = another z-score.</p>

<p>now convert z score to x score.
10 +/- answer x 0.2.</p>

<p>Basically just draw the graph out. You get 40% in the middle. Divide it by two. Add the 0.5.</p>

10

<p>A little easier way would be to use the empirical rule.
Like dannys717 said, most values are in the middle, approximately 34% on each side within 1 standard deviation.</p>

<p>You want about 20% on each side from the middle:
use 20/34 or .2/.34 = .5882
.5882(.2) = .1176</p>

<p>10 + .1176 = 10.117
10 - .1176 = 9.882</p>

<p>About .06 off from the real answer, but you should be able to eliminate the other choices since it is multiple choice.</p>

11

<p>Alright thanks for all the help! I understand now.</p>