Statistics

So, today we started off with a surprise quiz. How do you guys think you did? I decided to do the questions on the quiz we did. Well anyway, here's my scribe post.

1. A) Calculate the mean length and the standard deviation.

We found this one our calculator, by entering all our data (the 52 arrowheads) into our L1 by hitting [STAT] [1/Edit] and pinching in all 52 numbers under the L1 column. Don't forget to check your numbers just incase your numbers don't match the data. After that you hit [2nd] [QUIT] so you get back to the home screen. To get these stats you hit [2nd] [Vars] to get into your distribution menu. Then you hit [1] to get your 1-vars stats then hit [2nd] [L1] [Enter]. Your x bar is 25.44 and your σ is 5.62.

B) Determine the lengths of arrowheads one standard deviation below and one standard deviation above the mean?

In order to determine then lengths of arrowheads within 1σ below and above the mean you have to add and subtract µ from σ.

µ - σ = 19.82 (1σ below)

µ + σ = 31.06 (1σ above)

We have to find, how many arrowheads are between 20 abnd 31.

C) How many arrowheads are within one standard deviation of the mean?

In order to find how many arrowheads are between 20 and 31 you have to count how many arrowheads lie between those two numbers.

52 - 15 (the number of arrowheads that don't lie between 20 and 31) = 37.

D) What percent of the arrowheads are within one standard deviation of the mean length?

37/52 =0.7115 = 71.15%

The next question we've done before, but here's another recap..

2. A) A car designer designs car seats to fit women taller than 159.0 cm. What is the z-score of a woman who is 159.0 cm tall?

This is the formula to find the z-score. z = z-score, x = the value, µ = mean and σ = standard deviation.

159 is the value, 161.5 is the mean and 6.3 is the standard deviation.

-0.3968 is the z-score.

B) The manufacturer designs the seats to fit women with a maximum z-score of 2.8. How tall is a woman with a z-sccore of 2.8?

(z)(σ) + µ = x (this is the equation that Mr. K gave us)

To get this equation, you take the z-score equation and instead of having z by it's self, you get x by itself.

To do this, you take σ and multiply it by z, and then you take µ and move it to the other side which becomes positive, and then you get the equation (z)(σ) + µ = x.

Then you plug in the numbers into the equation:

(2.8)(6.3) + 161.5 = x

179.14 = x

Well this is the end of my scribe. Sorry it took so long. The next scribe is.. just_in.