Use substitution to solve the linear system of equations.
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Answer:
100% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,095 per month
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of $2,275 and a standard deviation of $290.
This means that
Sample of 65:
This means that
Finding the mean to be at least $2,095 per month
This is 1 subtracted by the p-value of Z when X = 2095. So
By the Central Limit Theorem
has a p-value of 0.
1 - 0 = 1
100% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,095 per month
First step is to get the average daily balance.
Take the sum of each day's balances.
If a payment has been made, the sign will be negative.
From Days 1 - 5 :
Day 1 = $200
Day 2 = $200
...
Day 5 = $200
That's $200 x 5 days = $1000
From Days 6 - 20 :
Day 6 = $350
Day 7 = $350
...
Days 20 = $350
That's $350 x 15 days = $5250
From Days 21 - 30 :
Day 21 = $150
Day 22 = $150
...
Day 30 = $150
That's $150 x 10 days = $1500
A total of :
$1000 + $5250 + $1500 = $7750
Now divide this total to the number of days to get the ADB or Average Daily Balance.
Next Step is to calculate for the finance charge using the formula :
where ADB is the average daily balance
r is the interest rate per day
d is the number of days or period given
From the problem, APR is 15.5%, it means that we need to divide the APR by 365 days.
So r = 0.155/365 = 0.000425
And we have d = 30 days
The charge will be :
Charge = 258.33 x 0.000425 x 30 = $3.29
The answer is $3.29