Sample of the reading scores of 35 fifth-graders has a mean of 82. The standard deviation of the population is 15. a. Find the best point estimate of the mean. b. Find the 95% confidence interval of the mean reading scores of all fifth-graders. c. Find the 99% confidence interval of the mean reading scores of all fifth-graders. d. Which interval is larger

a) 82

b) The 95% confidence interval of the mean reading scores of all fifth-graders is between 77 and 87.

c) The 99% confidence interval of the mean reading scores of all fifth-graders is between 75.47 and 88.53.

d) The 99% confidence interval is larger, due to the higher critical value of z.

Step-by-step explanation:

a. Find the best point estimate of the mean.

The best point estimate of the mean is the mean of the sample, which is 82.

b. Find the 95% confidence interval of the mean reading scores of all fifth-graders.

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 82 - 5 = 77

The upper end of the interval is the sample mean added to M. So it is 82 + 5 = 87

The 95% confidence interval of the mean reading scores of all fifth-graders is between 77 and 87.

c. Find the 99% confidence interval of the mean reading scores of all fifth-graders.

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 82 - 6.53 = 75.47

The upper end of the interval is the sample mean added to M. So it is 82 + 6.53 = 88.53

The 99% confidence interval of the mean reading scores of all fifth-graders is between 75.47 and 88.53.

d. Which interval is larger

The 99% confidence interval is larger, due to the higher critical value of z.

12*c

step-by-step explanation:

answer: the two figures are congruent.

step-by-step explanation: they're congruent because figure efgh is reflected across the x and y axis but it was also rotated.

hope it !