Answer:
The balance of account at the end of 36 years is $31,849.29
Step-by-step explanation:
We are given the following in the question:
P = $3,300
r = 6.5% = 0.065
t = 36 years
The compound interest is given by:
where A is the amount, p is the principal, r is the interest rate, t is the time in years and n is the nature of compound interest.
Since interest is compounded annualy we use n = 1
Thus, balance of account at the end of 36 years is $31,849.29
Answer:
So the value of height that separates the bottom 85% of data from the top 15% is 38.32.
C) 38.32
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Solution to the problem
Let X the random variable that represent the waiting time in minutes of a population, and for this case we know the distribution for X is given by:
Where and
And the best way to solve this problem is using the normal standard distribution and the z score given by:
We want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.85 of the area on the left and 0.15 of the area on the right it's z=1.04. On this case P(Z<1.04)=0.85 and P(z>1.04)=0.15
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 85% of data from the top 15% is 38.32.
C) 38.32
