Answer the question for each scenario by applying the rule of 72. How many years will it take each situation to double its money
2 answers:
Answer:
Matthew's money will double fastest in 6 years.
Step-by-step explanation:
In this question we have to calculate, how many years it will take each situation to double its money by the rule of 72.
formula = where R = Rate of interest
Situation A :
Matthew invests $5,000 in an account with a compound interest rate of 12%.
So = 6 years
It will take 6 years to double the investment.
Situation B :
Morgan invests $2,500 in an account with a compound interest rate of 8%.
So = 9 years
It will take 9 years to double the investment.
Situation C :
Maysen invests 10,000 in an account with a compound interest rate of 4.5%
So = 16 years
It will take 16 years to double the investment.
Matthew's money will double fastest in 6 years.
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Answer:
Step-by-step explanation:
Hello!
You have the variable
X: Area that can be painted with a can of spray paint (feet²)
The variable has a normal distribution with mean μ= 25 feet² and standard deviation δ= 3 feet²
since the variable has a normal distribution, you have to convert it to standard normal distribution to be able to use the tabulated accumulated probabilities.
a.
P(X>27)
First step is to standardize the value of X using Z= (X-μ)/ δ ~N(0;1)
P(Z>(27-25)/3)
P(Z>0.67)
Now that you have the corresponding Z value you can look for it in the table, but since tha table has probabilities of , you have to do the following conervertion:
P(Z>0.67)= 1 - P(Z≤0.67)= 1 - 0.74857= 0.25143
b.
There was a sample of 20 cans taken and you need to calculate the probability of painting on average an area of 540 feet².
The sample mean has the same distribution as the variable it is ariginated from, but it's variability is affected by the sample size, so it has a normal distribution with parameners:
X[bar]~N(μ;δ²/n)
So the Z you have to use to standardize the value of the sample mean is Z=(X[bar]-μ)/(δ/√n)~N(0;1)
To paint 540 feet² using 20 cans you have to paint around 540/20= 27 feet² per can.
c.
P(X≤27) = P(Z≤(27-25)/(3/√20))= P(Z≤2.98)= 0.999
d.
No. If the distribution is skewed and not normal, you cannot use the normal distribution to calculate the probabilities. You could use the central limit theorem to approximate the sampling distribution to normal if the sample size was 30 or grater but this is not the case.
I hope it helps!