You draw samples of size n from the population of all pennies in circulation. the random variable of interest is the mean age of the pennies in the sample (current year pennies are considered to be zero years old). the distribution of ages of pennies (starting at 0) is known to be skewed markedly to the right. that is, there are more recently minted pennies than older pennies in the population. one scholar claims that the mean age of all pennies in circulation is 7.4 years with a standard deviation of 3.3 years. assume that this scholar is correct. discuss the mean, standard deviation, and shape of the sampling distribution of sample means of the ages of pennies for each of the given sample sizes. where possible, give precise values. a. n = 5 b. n = 15 c. n = 40

Answers explained below

Step-by-step explanation:

Let X be the random variable that ages of pennies.

Also given that distribution of X is skewed to the right.

Given that,

mean = 7.4 years

standard deviation, sd = 3.3 years

Discuss the mean, standard deviation, and shape of the sampling distribution of sample means of the ages of pennies for each of the given sample sizes.

For n = 5,

the mean of the sampling distribution of mean = 7.4

sd of the samplong distribution of mean = 3.3 / sqrt(5) = 1.48

Shape of the distribution is positively skewed.

For n= 15

the mean of the sampling distribution of mean = 7.4

sd of the samplong distribution of mean = 3.3 / sqrt(15) = 0.85

Shape of the distribution is positively skewed.

For n = 40

the mean of the sampling distribution of mean = 7.4

sd of the samplong distribution of mean = 3.3 / sqrt(40) = 0.52

Shape of the distribution is bell shaped or normal distribution.

she played for 18.75 hours.

step-by-step explanation:

if she played 2/4 of a hour on tuesday. and there is 60 minutes in an hour and 60 divided by 4 is 7.5. and she played 2/4 of an hour on thursday then again 60 divided by 4 is 7.5, you add 7.5+7.5=56.25. now you have to do 1/4 of an hour, it equals 3.75. now you have to add them all up. 3.75+7.5+7.5=18.75

i hope this and i hope you get it right. it took me a while to get this done for you. : )

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.