Aproduct comes in cans labeled "38 oz". a random sample of 10 cans had the following weights:

{34.6, 39.65, 34.75, 40, 39.5, 38.9, 34.25, 36.8, 39, 37.2} with the following summary statistics:

n equals 10 space space top enclose x equals 37.465 space space s equals 2.27

estimate the true mean weight of the cans of product with 95% confidence.

a. 34, 41 ounces
b. 35.9, 39.1 ounces
c. 36.1, 38.9 ounces
d. 37.465 ounces

b. 35.9, 39.1 ounces

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 expressed a % 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".

barX=37.465 represent the sample mean for the sample  

population mean (variable of interest)

s=2.27 represent the sample standard deviation

n=10 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

barX +- t*[(s)/(sqrt{n))]   (1)

In order to calculate the critical value t we need to find first the degrees of freedom, given by:

df=n-1=10-1=9

Since the Confidence is 0.95 or 95%, the value of alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that t_(alpha/2)=2.26

Now we have everything in order to replace into formula (1):

37.465-2.26[(2.27)/(sqrt{10))]=35.9    

37.465+2.26[(2.27)/(sqrt{10))]=39.1

So on this case the 95% confidence interval would be given by (35.9;39.1)    

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.