1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
joja [24]
3 years ago
15

A fast-food restaurant has an automated beverage machine that dispenses a set amount of liquid based on a size setting. Suppose

that on the medium setting, the standard deviation of the amounts dispensed is Ï=17 mL . The manager of the restaurant plans on taking a sample of n medium drinks to construct 99\% percent confidence interval for the mean amount of liquid dispensed. They want the margin of error to be no more 10 mL
Mathematics
1 answer:
SashulF [63]3 years ago
8 0

Answer:

n=(\frac{2.58(17)}{10})^2 =19.24 \approx 20

So the answer for this case would be n=20 rounded up to the nearest integer would be the sample required to obatin a margin of erros or 10 ml at 99% of confidence

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".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma =17 represent the population standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =10 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.005;0;1)", and we got z_{\alpha/2}=2.58, replacing into formula (b) we got:

n=(\frac{2.58(17)}{10})^2 =19.24 \approx 20

So the answer for this case would be n=20 rounded up to the nearest integer would be the sample required to obatin a margin of erros or 10 ml at 99% of confidence

You might be interested in
Of the 35 students in my class, 11 practice karate, 11 play piano, and 20 take math lessons. $ students play piano and go to mat
Andrews [41]
There are twenty four students that do all
4 0
2 years ago
Read 2 more answers
2y+3=-2x written in slope intercept form
Alex777 [14]
Y=-x-3/2
That's it written in slope intercept form
3 0
3 years ago
2(m-3)+7<21 PLEASE HELP!!!
Contact [7]

Simplify. Distribute 2 to all terms within the parenthesis

2(m -3) = 2m - 6

Simplify. Combine like terms

2m - 6 + 7 < 21

2m + 1 < 21

Isolate the m. Subtract 1 from both sides

2m + 1 (-1) < 21 (-1)

2m < 20

Isolate the m. Divide 2 from both sides

2m/2 < 20/2

m < 20/2

m < 10

m < 10 is your answer

hope this helps

4 0
2 years ago
List the next 4 multiples of the unit fraction . 1/2 ___,___,___,___,
const2013 [10]
½ × 2 = 1
½ × 3 = 3/2
½ × 4 = 2
½ × 5 = 5/2
8 0
3 years ago
Read 2 more answers
HURRY SOMEONE PLEASE HELP ME??!!!!!!!
goblinko [34]

Answer:

The answer is A hope it helps!

7 0
3 years ago
Other questions:
  • Two containers filled with water are leaking. Container A leaks at a rate of 1/4 gallon per hour. Container B leaks at a rate of
    9·1 answer
  • Find two numbers whose sum is 67 and whose difference is 13
    14·2 answers
  • For any three consecutive numbers, what can you say about odd numbers and even numbers?Explain
    5·1 answer
  • Anybody know this answer
    5·1 answer
  • Simplify: Negative two and one-third minus negative ten and one-sixth(20 points)
    10·1 answer
  • Please Help!!!!
    10·1 answer
  • Explain to me in words how you would find the slope of this line and explain your answer
    11·2 answers
  • I’m not sure how to do this please help!
    12·1 answer
  • Recall that two angles are complementary if the sum of their measures is 90°. Find the measures of two complementary angles if o
    12·1 answer
  • ip a standard sheet of paper measures 8 1/2 by 11 inches. find the area of one such sheet of paper in
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!