3. After came back from the statistic class of Mr.K He started gather the data about the milk of his cows in a month, and he made this table
4.
5. Oki… lets start ….. Question a. “ Is the data approximates the normal distribution? Using the probabilities of the normal distribution .” 1 σ 2 σ 3 σ Remember Standard Normal Distribution curve! To determine . We need to imagine that the number of cow should lay on x-axis and the number of milk should lay on the y-axis Number of Cow Number of Milk So….
6. We need to calculate the mean( μ ) and standard deviation ( σ ) base on the data of Milk and Cows ! To calculate mean and standard deviation, we can use the calculator: List 2 List 1 We put the number of cow to List 2 and the number of Milk to List 1 Use 1-Var stats to calculate σ and μ : [stat] => CALC => 1-Var Stats => [ENTER] And set up the screen like this …
7.
8. And now, we have mean and standard deviation, Lets calculate 1 σ , 2 σ , and 3 σ 1-Standard deviation : Max: + =20.7 Min: - =17.12 So the Cows which give the milk between 17.12L and 20.7L .. uhmm lets count …There are 153 Cows 2-Standard deviation : Max: + 2 =20.7 Min: - 2 =17.12 3-Standard deviation : Max: + 3 =20.7 Min: - 3 =17.12 There are 193 Cows There are 209 Cows
9. After that, we change the number of Cows to %, because we want to compare with “68-95-99 rule” 1-Standard deviation : 2-Standard deviation : 3-Standard deviation : 153 /209=73.2% We know total of the Cows : 209 Cows 193 /209=92.34% 209 /209=100% Base on “68-95-99 rule” the data approximates the normal distribution To be..continue =>
10. …… Time to Party ^_^! And now…. B /Mr.K makes a small party in his class. CowMilk decided that he will kill all of the cows which give him less than 50% of the normal milk to make the steaks and get milk from the cows which give him greater than 80% of the normal. What is the number of cows he will use?
11. When solve any kind of this question, we usually need a GRAPH Because we know that the data approximates the normal distribution (question a/) . We can make a graph “… he will kill all of the cows which give him less than 50% of the normal milk… “ “… get milk from the cows which give him greater than 80% of the normal…” The question give us the %, we need to change it to the z-score to put on the graph !
12. To convert from % to Z-score, we use the calculator to convert : [2 ND ] => [VARS] => invNorm( => [ENTER] And then put 0.80 (80%) => [ENTER] The calculator will give us z-score of 0.80(80%) , this is 0.84162 0.84162 So on for 50% REMEMBER put invNorm(0.5) in the calculator We will have z-score of 0.50(50%) = 0 0
13. 0.84162 0 “… get milk from the cows which give him greater than 80% of the normal…” “… he will kill all of the cows which give him less than 50% of the normal milk… “ Look at the question So, look at the graph, we will see the cows he will use The Cows he will use
14. Use this formula, we can calculate the volume of milk (X) at 2 points on the graph mean Z-score Volume of milk We all know Z , , mean => we calculate X X 50 =18.913 X 80 =20.41 And the pull out the table and…count => The number of the cows he use : 8+11+21+45+18+8+8 =119 Cows
15.
16. Can I borrow 300 000$ to buy that Car ? Uhmmm…we offer the loan with 7.5% annually interest for 5 years, compound monthly Ok !! Supercar
17.
18.
19. After that, he take his calculate and use TVM solve to calculate the monthly payment which can be offered by the bank: TVM solve : [APPS] => Finance…=> TVM solve => payment/month =$ 6011.38 Total payment : $6011.38 * 60 = $360682.8
20.
21. Consider 2 results, we can know the difference : $360682.8 - 346936.2 =$ 13749.6 SO…if he use all the money from selling the milk, he can make 46.8 ~ 47 payments ( 47/12 ~4 years) and save $13749.6 !!! He should do it.. I mean.. I should do it ^^
![[object Object],Boss of Milk-Cow Farm All of the calculations base on TI-84 Plus](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)