Question

The ages of five randomly chosen cars in a parking garage are determined to be​ 7, 9,​ 3, 4, and 6 years old. If one considers this sample of 5 in groups of​ 3, what is the probability of the population mean falling between 5.5 and 6.5​ years?

Answer 1

The question requested the calculation of the probability for a group mean with insufficient information. For a uniform distribution with given range, the probability density function is provided, but additional data like the distribution of ages is required to determine the actual probability for the student's inquiry.

Step-by-step explanation:

The student's question pertains to the probability of selecting groups of three cars whose mean age falls between 5.5 and 6.5 years. To compute this probability, we would normally use the sampling distribution of the mean. However, the question doesn't provide enough information to calculate the exact probability since we do not have the distribution parameters (such as the mean and standard deviation) of the ages of all cars in the parking garage. If we assume that the mean and standard deviation of ages are known, and that they follow a normal distribution as per Central Limit Theorem for sufficiently large samples, we would use the z-score formula to find the probability. Unfortunately, without this information, we cannot provide the probability as requested.

If the age of cars in the staff parking lot is uniformly distributed from 0.5 to 9.5 years, the probability density function (f(x)) for a continuous uniform distribution is defined as f(x) = 1 / (b - a) where 'a' and 'b' are the minimum and maximum values of the interval respectively. In this case, a = 0.5 and b = 9.5, so the probability density function would be f(x) = 1 / (9 - 0.5). For the third quartile (Q3) of ages of cars in the lot, we would find the value of 'x' such that the cumulative distribution function (CDF) upto that point is 0.75.

Answer 2

the answer is 4 out of 10 or 4/10 = 0.4

Step-by-step explanation:

from the question which says that the ages of five randomly chosen cars in a parking garage are determined to be​ 7, 9,​ 3, 4, and 6 years old. If one considers this sample of 5 in groups of​ 3

solution

the number of groups of 3 that are possible implies that

5 choose 3 = 10 possible groups of 3

also,

the number of these groups of 3 that have a true mean of more than 6years needs to be considered.

The following groups add up to 19 or more ; (9,7,6), (9,7,4), ( 9,7,3) , (9,7,4).

therefore the answer is 4 out of 10 or 4/10 = 0.4