Based on the information from Consumer Reports, a random sample of 86 thirty-gram servings of Duncan Hines Chocolate Chip Cookies had a sample means of 132 calories with a sample standard deviation of 27 calories. A random sample of 75 Pepperidge Farm Chocolate Chip Cookies has a sample mean of 124 calories with sample standard deviation of 33 calories. Build an 80% confidence interval for the true mean difference in calories for these two cookie brands.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a  population value with a certain degree of confidence. It is often expresseda % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

For this case we have the following info given:

mean for Duncan Hines Chocolate Chip Cookies

represent the sample size for Duncan Hines Chocolate Chip Cookies

represent the deviation for Duncan Hines Chocolate Chip Cookies

mean for Pepperidge Farm Chocolate Chip Cookies

represent the sample size for Pepperidge Farm Chocolate Chip Cookies

represent the deviation for Pepperidge Farm Chocolate Chip Cookies

Solution to the problem

The degrees of freedom for this case are:

Since the Confidence is 0.80 or 80%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.1,159)".And we see that

The confidence interval is given by:

And replacing we got:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

x-3y=4

step-by-step e