The solution to the query
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:
a) 0.00019923%
b) 47.28%
Step-by-step explanation:
a) To determine the likelihood that all sockets in the sample are defective, we can use the following approach:
The first socket is among a group that has 5 defective out of 38, leading to a probability of 5/38.
The second socket is then taken from a group of 4 defective out of 37, following the selection of the first defective socket, resulting in a probability of 4/37.
Extending this logic, the chance of having all 5 defective sockets is computed as: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%.
b) Using similar reasoning as in part a, the first socket has a probability of 33/38 of not being defective as it's chosen from a set where 33 sockets are functionally sound. The next socket has a proportion of 32/37, and this continues onward.
The overall probability calculates to (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%.
Answer: refer to the image
Step-by-step explanation:
Answer:
The converse is:
If the ratio of left-handers to right-handers is 1: 8, then for every 3 left-handed individuals, there are 24 right-handed individuals.
The truth value is: True
Step-by-step explanation:
This statement can be expressed as:
p -> If a class contains 3 left-handed individuals and 24 right-handed individuals,
q -> the ratio of left-handed to right-handed individuals is 1:8.
The converse of a conditional statement is:
if q then p.
Thus, we have the converse as:
if the ratio of lefties to righties is 1: 8, then for each 3 left-handed individuals, there are 24 right-handed individuals.
The truth value is as follows:
For p, we find the ratio = 3: 24,
which simplifies to.
Ratio = 1: 8.
For q, we have:
Ratio = 1: 8.
Since both conditions are accurate, the truth value is true.
