Complete Question
The complete question appears in the first uploaded image
Answer:
a) Yes, selecting 15 corresponds to a binomial experiment
b)
c)
d) 
Step-by-step explanation:
Regarding question a:
For an experiment to qualify as binomial
the trials have to be independent
each trial must yield one of two possible outcomes
Given that the selection of 15 individuals is random, we ascertain that the trials are independent and the outcomes are “either the individual saves for retirement or does not save for retirement.”
Therefore, we conclude that the selection of 15 people at random is indeed a binomial experiment.
In question b:
The probability that all selected adults do not save for retirement is mathematically modeled as
Here C signifies combination
r = 15 implies all selected adults
n refers to the population size equating to 15
From the problem, p = 0.20
and q can be calculated as
=>
=> 
Thus
Regarding question c:
The probability that exactly five of the selected adults do not save for retirement is mathematically modeled as
In relation to question d:
The probability that at least one of the selected adults opts not to save for retirement can be mathematically expressed as
![P(r \ge 1 ) = 1 - [ ^{15} C _ 0 * (0.20)^{0} * (0.80 )^{15}]](https://tex.z-dn.net/?f=P%28r%20%5Cge%201%20%29%20%3D%20%201%20-%20%5B%20%5E%7B15%7D%20C%20_%200%20%2A%20%20%280.20%29%5E%7B0%7D%20%2A%20%280.80%20%29%5E%7B15%7D%5D)
To calculate the monthly interest, take the APR and divide it by 360, then multiply the result by 30 days. Typically, each loan is backed by the vehicle that was purchased, hence we will utilize the secured APR.
8. For an average secured APR of 5.85%, the calculation is: 5.85% divided by 360 multiplied by 30 gives a monthly rate of 0.4875%.
The vehicle cost is 19,725; with a sales tax of 4.75% and a down payment of 2,175.
19,725 multiplied by 1.0475 results in 20,661.94, and after subtracting the down payment, the loan amount is 18,486.94.
To find the accrued interest for the first month: 18,486.94 multiplied by 0.4875% equals 90.12.
9. An excellent secured APR of 4.80% results in a monthly rate of 0.40% when 4.80% is divided by 360 and multiplied by 30.
Price of a different vehicle: 15,867; a sales tax of 5.25%; down payment equals 10% of the total.
Calculating, 15,867 multiplied by 1.0525 gives 16,700.02; taking 90% results in a principal balance of 15,030.02 at the loan's beginning.
10. For a fair secured APR at 7%, dividing by 360 and multiplying by 30 provides a monthly rate of 0.5833%.
Cost of a new vehicle is 19,072; sales tax stands at 4.5%; down payment of 1,200.
Cost for a used vehicle is 15,365; same tax and down payment as the new one.
Calculating for new: 19,072 multiplied by 1.045 results in 19,930.24, with down payment deducted gives 18,730.24.
Accrued interest for new is 18,730.24 multiplied by 0.5833% equating to 109.25.
For the used vehicle: 15,365 multiplied by 1.045 results in 16,056.43, then down payment leaves 14,856.43.
Accrued interest here is 14,856.43 multiplied by 0.5833% equaling 86.66.
The difference in interest accrued by the first month's end is 109.25 minus 86.66, which is 22.59.
A) To establish a sampling plan, follow these 5 steps:
1) Identify the sample population: which customers will you reach out to?
Those who purchased a new car during a specific year.
2) Determine the population size: how many customers will you contact?
From the 30,000 car buyers, select 1,000 customers to contact.
3) Select contact method: what is your means of contacting customers?
Since you have a list with names and addresses, mailing questionnaires is feasible.
4) Define the sampling frame: what is the timeline or deadline for contacting customers?
Send out questionnaires and allow two months for responses.
5) Decide on the analysis approach: is your research qualitative or quantitative?
You aim for quantitative research, so you will use probabilistic sampling.
B) The 32.5% probability relates only to those customers who experienced mechanical issues, specifically power door lock problems, and does not account for those without any problems or those reporting issues after the first 5,000 miles.
C) To estimate the probability of power door lock problems among all customers within the first 5,000 miles, consider the entire sample:
P = 13 / 1000 = 0.013
Therefore,
N = 0.013 × 30,000 = 390
Thus, the estimated number of new cars that had power door lock issues within 5,000 miles is 390.
Answer:
4
Step-by-step explanation:
Each sandwich costs 6 dollars, while chips sell for 3 dollars. She purchased 5 sandwiches at 6 dollars each, amounting to 30 dollars (5*6=30). This leaves her with 12 dollars to use since her total expenditure was 42 dollars. Given that chips are 3 dollars each, with 12 dollars left, 4 bags could be bought (4 * 3 = 12).
