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
givi [52]
2 years ago
9

A cola-dispensing machine is set to dispense 8 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manufacturer

of the machine would like to set the control limit in such a way that, for samples of 34, 5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit.
a. At what value should the control limit be set? (Round z values to two decimal places. Round your answers to 2 decimal places.)
b. If the population mean shifts to 7.6, what is the probability that the change will be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
c. If the population mean shifts to 8.7, what is the probability that the change will be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
Mathematics
2 answers:
pshichka [43]2 years ago
5 0

Answer:

Step-by-step explanation:

Hello!

The variable of interest is X: ounces per cup dispensed by the cola-dispensing machine.

The population mean is known to be μ= 8 ounces and its standard deviation σ= 1.0 ounce. Assuming the variable has a normal distribution.

A sample of 34 cups was taken:

a. You need to calculate the Z-values corresponding to the top 5% of the distribution and the lower 5% of it. This means you have to look for both Z-values that separates two tails of 5% each from the body of the distribution:

The lower value will be:

Z_{o.o5}= -1.648

You reverse the standardization using the formula Z= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } } ~N(0;1)

-1.648= \frac{X[bar]-8}{\frac{1}{\sqrt{34} } }

X[bar]= 7.72ounces

The lower control point will be 7.72 ounces.

The upper value will be:

Z_{0.95}= 1.648

1.648= \frac{X[bar]-8}{\frac{1}{\sqrt{34} } }

X[bar]= 8.28ounces

The upper control point will be 8.82 ounces.

b. Now μ= 7.6, considering the control limits of a.

P(7.72≤X[bar]≤8.28)= P(X[bar]≤8.28)- P(X[bar]≤7.72)

P(Z≤(8.28-7.6)/(1/√34))- P(Z≤7.72-7.6)/(1/√34))

P(Z≤7.11)- P(Z≤0.70)= 1 - 0.758= 0.242

There is a 0.242 probability of the sample means being between the control limits, this means that they will be outside the limits with a probability of 1 - 0.242= 0.758, meaning that the probability of the change of population mean being detected is 0.758.

b. For this item μ= 8.7, the control limits do not change:

P(7.72≤X[bar]≤8.28)= P(X[bar]≤8.28)- P(X[bar]≤7.72)

P(Z≤(8.28-8.7)/(1/√34))- P(Z≤7.72-8.7)/(1/√34))

P(Z≤-2.45)- P(Z≤-5.71)=0.007 - 0= 0.007

There is a 0.007 probability of not detecting the mean change, which means that you can detect it with a probability of 0.993.

I hope it helps!

Tresset [83]2 years ago
4 0

Answer:

a) ( -1.65 ≤ Z ≤ 0.39)

b) 0.3446

c) 0.658

Step-by-step explanation:

Let X be the random variable set to dispense cola per cup; α be standard deviation; U be the mean.

a) P(X > 8) = 0.35

P(X ≤ 8) = 0.65

P(X - U/α ≤ 8 - U) = 0.65

P(Z ≤ 8 - U) + 0.5 = 0.65

P(0 ≤ Z ≤ 8 - U) = 0.65 - 0.5 = 0.15        

Using table: 8 - U = 0.39

P(X > 8) = 0.05

P(X ≤ 8) = 0.95

P(X - U/α ≤ 8 - U) = 0.95

P(8 -U ≤ Z ≤ 0) + 0.95 = 0.5

P(8 - U ≤ Z ≤ 0) = -0.45

Using the table: 8 - U = 1.65  

∴ The control limit is ( -1.65 ≤ Z ≤ 0.39)

b) P(X≤8) = P(X - U/α ≤ X - 7.6)

= P( Z ≤ 8 - 7.6)

= P( Z ≤ 0.4) = 0.5 + 0.1554 = 0.6554

P( X > 8) = 1 - 0.6554 = 0.3446  

c) P(X ≤ 8) = P(X - U/α ≤ X - 8.7) = 0.65

= P(Z ≤ 8 - 8.7)

= P(Z ≤ -0.7) = 0.5 - 0.2580 = 0.3420

P(X > 8) = 1 - 0.3420 = 0.6580                    

You might be interested in
PLEASE HELP ITS URGENT how can you use an equation to make a prediction from a pattern?
allochka39001 [22]
An equation can be used to predict values from a pattern by merely substituting any value to determine the equivalent value. An example is the geometric series which has a standard equation of an = a1 * r^(n-1) and is used to predict the nth term of the series
4 0
3 years ago
Which expression is equivalent to 5(2+7)?
frosja888 [35]

Answer:

I can help you but first I need the rest of the answers to find out what's it equivalent to.

4 0
3 years ago
Becky is planning a 2 100-mile trip to St. Louis to visit a college. Her car averages 30 miles per gallon
GaryK [48]

Answer:

70

Step-by-step explanation:

3 0
2 years ago
Ten tiles numbered 1 through 10 are turned face down. One tile is turned up at random, and a die is rolled and the number is squ
attashe74 [19]

Answer:

18.33333333%. Please mark as brainliest if I’m Correct. :)

Step-by-step explanation:

5 0
2 years ago
Please can you guy help for this questiong
ad-work [718]

Answer:

Reason 1. Given

Statement 2. <CAD is congruent to <BAD

Reason 2. Definition of angle bisector

Statement 3. Segment AD is congruent to segment AD

Reason 4. All right angles are congruent

Reason 5. ASA

4 0
2 years ago
Other questions:
  • Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small
    6·1 answer
  • Solve system by subsubstitution?<br> 14x-2y=46<br> -7x+y=-23
    12·1 answer
  • 0.11 as a fraction and in the simplest form
    15·2 answers
  • If h(x) = 6 – x, what is the value of (h circle h) (10)?
    6·1 answer
  • What is the correct?
    12·1 answer
  • I need help asap<br> i need to know how to show work pls help
    6·1 answer
  • 21. Which is the correct answer
    11·1 answer
  • Find the value of x that makes the equation true:<br><br>x + 3 = 4
    11·1 answer
  • Whats 12 plus 4 .... get duh hints
    5·1 answer
  • Make an accurate drawing of two rectangles with the same perimeter, but different areas. Indicate the dimensions of the rectangl
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!