Answer:
Shown below
Step-by-step explanation:
I believe that the number machine would look like this:
number of hours x (£15) + (£25)
To get the z-value of the scores of the four students, we are going to use the formula for standard score or z-score. It is score minus the mean score, then divided by standard deviation.
z= Score (X)-Mean / SD
To find the z-value of each score, we have to use a Z table. Using the z-score, we are to look first at the y-axis of the table which will highlight the first two digits of the z-score. Then, the x-axis for the second decimal place of the z-score.
You can use this as reference for the z-table: http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf
Mean= 500SD= 100Scores= 560, 450, 640, 530
For the student who scored 560,z= X-Mean / SDz= 560-500 / 100z= 60 / 100z= 0.6
The score is 0.6 standard deviation above the mean. The z-value is 0.7257 or 72.57%.
For the student who scored 450,z= X-Mean / SDz= 450-500 / 100z= -50 / 100z= -0.5
The score is -0.5 standard deviation above the mean. The z-value is 0.3085 or 30.85%.
For the student who scored 640,z= X-Mean / SDz= 640-500 / 100z= 140 / 100z= 1.4
The score is 1.4 standard deviation above the mean. The z-value is 0.9192 or 91.92%.
For the student who scored 530,z= X-Mean / SDz= 530-500 / 100z= 30 / 100z= 0.3
The score is 0.3 standard deviation above the mean. The z-value is 0.6179 or 61.79%.
Continuous compounding is the mathematical limit that compound interest can reach.
It is the limit of the function A(1 + 1/n) ^ n as n approaches infinity. IN theory interest is added to the initial amount A every infinitesimally small instant.
The limit of (1 + 1/n)^n is the number e ( = 2.718281828 to 9 dec places).
Say we invest $1000 at daily compounding at yearly interest of 2 %. After 1 year the $1000 will increase to:-
1000 ( 1 + 0.02/365)^365 = $1020.20
with continuous compounding this will be
1000 * e^1 = $2718.28
Subtract the amount she has saved from the price of the laptop:
849 - 232 = 617
Now divide the amount she still needs by the amount she saves per week:
617 / 28 = 22.04
Because the answer has a number to the right of the decimal, she will need to save for 23 full weeks to have enough money.
If she saves for 22 weeks, she would be $1 short:
22 x 28 = 616 + 232 = 848
