Math 227 Answers for Computer Lab Review 1 Chapters 2-6

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1 ) A) Pie Chart Figure Figure 2 a) Enter values in A:A, Data labels in B:B (Fig 2) b) Click on Chart Wizard, select Pie, then Next c) Click on the Series Tab, then click on the Add button. d) Enter the Chart description in the Name field e) Enter the data values in the Values field f) Enter the labels in the Category (X) axis labels field (see figure ) g) Click on Next; Click the Legend tab and deselect the Show legend checkbox h) Click the Data Labels tab and check the Show label and percent checkbox. i) Click on Finish B) Pareto Chart a) Click on Chart Wizard, select Column, then Next b) Click on the Series Tab, then click on the Add button. c) Enter the Chart description in the Name field d) Enter the data values in the Values field e) Enter the labels in the Category (X) axis labels field (see figure 3) f) Click on Next; Click the Legend tab and deselect the Show legend checkbox g) Click on Titles tab and enter Degree in Category (X) axis field and Number in Value (Y) axis field. (see fig 4) h) Click finish i) Double click inside any of the vertical bars. j) In the window that opens select the Options tab, then set the Gap Width value to. k) click ok l) Next we need to sort the data in Descending order. m) Select the range A:B n) Click on the Data tab, select Sort, choose column A, check the Descending check box, then OK. o) The resulting graph should look like the one in Figure. /2/27

2 Figure 4 Figure 3 Pareto Chart for College Degrees Number B H E M A P Degree Figure 2 /2/27

3 Enter data in A2:A2 a) Enter Labels Mean, Median, as shown below: b) Figure c) In cell B23 (next to the label Mean) enter: =AVERAGE(A2:A2) d) In cell B24 (next to the label Median) enter: =MEDIAN(A2:A2) e) In cell B2 (next to the label Range) enter: =MAX(A2:A2) MIN(A2:A2) f) In cell B2 (next to the label Standard Deviation) enter: = STDEVP(A2:A2) (Format the cell A2 by: Select cell, right-click, select Format cells, click on Alignment tab, check the Wrap Text checkbox, then ok.) g) Round Standard Deviation to decimal position: in cell B27 enter: =ROUND(B2,) h) Calculate width: in Cell B29 (next to the label Width) enter: =B2/ (range divide by number of classes) i) Roundup result: In cell B3 enter: =ROUNDUP(B29,) j) Thus, the Width (to be used in creating the Frequency distribution) is 9. Create Frequency Distribution: Follow procedure detailed in the EXCEL Guide, pages 2 and 3. The result should look like this: 3 /2/27

4 Frequency Histogram Figure 7 In order to create the various graphs, follow the procedures detailed in the EXCEL Guide, page 7. The results should look like the following: Frequencies Classes Figure 8 Notes:. The Values range is F2:F7 (I included one additional - F7 - dummy frequency at the end in order to make the graph look better 2. The Category (X) axis labels range is E2:E7 3. For esthetics purpose, I adjust the slant of the x-axis labels, after the graph was done: Double-click on any of the labels; on the Format axis window, select the Alignment tab, then set the degrees to a value of 4. 4 /2/27

5 Frequency Polygon Ogive Figure 9 Figure 2) Counting Rules: Factorial: Excel Function: (Math): FACT Permutation: Excel Function: (Stat): PERMUT Combination: Excel Function: (Math): COMBIN Examples a) Number of ways to select 7 objects out of 3 when the order matters: Formula: 3 P 7 Result: 3,23,8, b) Number of ways to select objects out of 34 when the order does not matter: Formula: 34 C Result:,344,94 c) factorial divided by factorial Formula:! /! Result:,8,24,4 3) A survey found that out of 7 teenagers play video games. teenagers are selected at random. What is the probability that among the selected teens, at least 4 play video games (use the formula: X n X P( exactly X ) = C p q ). n X ( ) ( ) 2 p =, q =, n = 7 7 P( X = 4 or X = ) = P( X = 4) + P( X = ) 4 P 2 ( X = 4) = C 4 = P 2 ( X = ) = C = P(At least 4) = =.4 ( EXCEL: =COMBIN(,4)*((/7)^4)*(2/7) or =BINOMDIST(4,,/7,False) /2/27

6 4) USE of NORMSDIST, NORNSINV, NORMDIST, NORMINV ) Find the probability for the standard normal variable z using EXCEL built-in functions a. P(z <.47) = NORMSDIST(.47) =.9292 b. P(.2 < z < 2.7) = NORMSDIST(2.7) - NORMSDIST(.2) = =. c. P(z > -.2) = - NORMSDIST(-.2) =.3 =.98 ) Find z given a. P to the right of z is.7 P to the left is :.7 =.2844 z = NORMSINV(.2844) = -.7 b. P to the left of z is.2 z = NORMSINV(.2) = -.4 7) The average number of passengers on the flights between Los Angeles and New York is 23. Suppose that the distribution is approximately normally distributed with σ =. Find the probability that a randomly selected flight will have (using Excel built-in functions): a. Between 2 and 22 passengers. NORMDIST(22,23,,TRUE) - NORMDIST(22,23,,TRUE) = =.938 b. Less than 24 passengers. NORMDIST(24,23,,TRUE) =.747 c. More than 23 passengers. - NORMDIST(23,23,,TRUE) =.3949 =. 8) A researcher in a new cholesterol drug trial wants to select people in the upper and lower 2% of the population based on their cholesterol level. Assume that the distribution is normal with a mean cholesterol value of 2 and a standard deviation of 2. Find the range of cholesterol levels that people should have in order to qualify for the study. (Use Excel Built-in functions). 2% 2% σ = 2 Use the NORMINV Excel function: z = NORMINV(.2,2,2) = 83.7 z 2 = NORMINV(.8,2,2) = 2.83 z 2 z 2 /2/27

7 9) A chocolate factory produces chocolate bars with a mean weight of 8 oz and a standard deviation of. oz. If 2 chocolate bars are selected at random, what is the probability that they will weight less than 7.9 oz or more than 8. oz. What will this probability be if only bars are selected? This problem deals with the probability of the mean for a sample. There is not Excel function to fully automated this type of problem. We need to use the transformation formula X µ z = and then use the NORMSDIST function to calculate the probability. σ n?? σ = z X µ X µ 8. 8 = = = 2.98 z2 = = = 2.98 σ n. 2 σ n. 2 P(z < -2.98) = NORMSDIST(-2.98) =.4 P(z > 2.98) = - NORMSDIST( 2.98) =.4 ANSWER for n = 2:.28 Repeat above process for n = : z X µ X µ 8. 8 = = = 2. z2 = = = 2. σ n. σ n. P(z < -2.) = NORMSDIST(-2.) =.74 P(z > 2.) = - NORMSDIST( 2.) =.74 ANSWER for n = :.248 Notes:. In the use of the NORMDIST Excel function, use TRUE as the value for the last parameter. 7 /2/27