MATH 1318/11

LAB 6

The goal of this lab is to standardize data, to compute probabilities using the standard normal distribution, and to find values given probabilities.

(2 points) 1.Use Minitab to compute the mean and standard deviation of your RAW V3 data (as listed in Lab 1). The Minitab instructions are the same as in Lab 3.

Mean______

Standard deviation ______

2.What are the mean and standard deviation you computed in Lab 3, Part 2?

Mean______

Standard deviation ______

Are these values close to those in question 1? Explain clearly why they could be different.

______

______

*** For the remainder of the labs, use the mean and standard deviation from question 1****

(1 point) 3.Sort the list of 40 data values from smallest to largest, using the Minitab directions below. Write down the raw scores on lines #1, #20, and #40. Compute the corresponding z-scores by using the formula. Round to two decimal places.

Line # / x value / z - score / Value in table 4
1 / Low value (L) =
20 / Middle Value (M) =
40 / High Value (H) =

(1 point) 4.Using the mean and standard deviation from #1 above, and using the formula , find the data value x that goes with the following z-scores. Use and .

z – score / x value

For the rest of the lab, you will make the assumption that your data is approximately normally distributed. For some students this is a reasonable assumption; for others, it is not. If you have any questions about this, please see your instructor. Each problem from 5 – 10 is worth 1 point.

5. a) Sketch a normal curve with your value for as .

b) Locate your low x value (L) and your high x value (H) on the x axis.

c) Shade the area between x = L and x = H.

d) Use the values from the tables in #3 to find the shaded area.

e) Find P(L < x<H). ______

6. a) Sketch a normal curve with your value for as .

b) Locate your middle x value (M) and your high x value (H) on the x axis.

c) Shade the area between x = M and x = H.

d) Use the values from the tables in #3 to find the shaded area.

e) Find P(M < x<H). ______

7. a) Sketch a normal curve with your value for as .

b) Locate your middle x value (M) on the x axis.

c) Shade the area to the left of x = M.

d) Use a value from the tables in #3 to find the shaded area.

e) Find P( x < M). ______

8. a) Sketch a normal curve with your value for as .

b) Locate your high x value (H) on the x axis.

c) Shade the area to the right of x = H.

d) Use a value from the tables in #3 to find the shaded area.

e) Find P( x> H). ______

9 a) Sketch a normal curve using your value for .

b) Shade the area where the lowest 10% of your values would be.

c) What is the z – score for this area. ______

d) Using the method from #4 above, find the value

e) Use this information to fill in the blanks. The first blank should be your name for

"10% of all ______in my population are below ______."

10 a) Sketch a normal curve using your value for .

b) Shade the area where the top 5% of your values would be.

c) What is the z – score for this area. ______

d) Using the method from #4 above, find the value

e) Use this information to fill in the blanks. The first blank should be your name for

"5% of all ______in my population are above ______."

Minitab Directions

to sort your list of data values:

Data

Sort

select V3

by column (c3 if that is the location of V3)

Store in column of current worksheet (pick a column that is empty.)

OK

1