Suppose samples of size n = 16 are selected from a population with mean 80 and standard deviation 8. State the mean, standard error, and distribution of the sampling distribution of the sample mean.

(i) The mean is:

5.008 80cannot be determined.
(ii) The standard error is:0.802.00 8cannot be determined.
(iii) The shape of the distribution:
is normal because the population is normal. is approximately normal by the Central Limit Theorem. cannot be determined.

Step-by-step explanation:

(a)

(i)

The mean is 80

The mean of the sampling distribution of the mean will be the same as the mean of the population

(ii)

The standard error is

∅√n=8/√16 = 2

(iii) The shape of the distribution:

cannot be determined.

The sample size is too small to determine the shape of the distribution using CLT

(b)

(i)

The mean is 80

The mean of the sampling distribution of the mean will be the same as the mean of the population

(ii)

The standard error is

∅/√n=8/√100 = 0.8

(iii) The shape of the distribution:

is approximately normal by the Central Limit Theorem.

Since the sample size is 100, therefore we can approximate the distribution of the sample means as normal by CLT.

(c)

(i)

The mean is 80

The mean of the sampling distribution of the mean will be the same as the mean of the population

(ii)

The standard error is

∅/√n=8/√16 = 2

(iii) The distribution:

is normal because the population is normal

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204