HELP ME PLEASE, GONNA GIVE 25 POINTS!!

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

pshichka [43]

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!

5 0

3 years ago

Read 2 more answers

I need answer Immediately pls!!!!!!

Illusion [34]

Given:

Total number of students = 27

Students who play basketball = 7

Student who play baseball = 18

Students who play neither sports = 7

To find:

The probability the student chosen at randomly from the class plays both basketball and base ball.

Solution:

Let the following events,

A : Student plays basketball

B : Student plays baseball

U : Union set or all students.

Then according to given information,

$n(U)=27$

$n(A)=7$

$n(B)=18$

$n(A'\cap B')=7$

We know that,

$n(A\cup B)=n(U)-n(A'\cap B')$

$n(A\cup B)=27-7$

$n(A\cup B)=20$

Now,

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

$20=7+18-n(A\cap B)$

$n(A\cap B)=7+18-20$

$n(A\cap B)=25-20$

$n(A\cap B)=5$

It means, the number of students who play both sports is 5.

The probability the student chosen at randomly from the class plays both basketball and base ball is

$\text{Probability}=\dfrac{\text{Number of students who play both sports}}{\text{Total number of students}}$

$\text{Probability}=\dfrac{5}{27}$

Therefore, the required probability is $\dfrac{5}{27}$ .

3 0

3 years ago

Which represents a value 1/10 of 0.7?

Nastasia [14]

0.7 can also be written as 7/10. All you need to do is multiply 7/10 by 1/10. You will get 7/100 which is 0.07

3 0

3 years ago

Read 2 more answers

Plssss help what is x

makvit [3.9K]

Answer:

x = 4

Step-by-step explanation:

If you do not want to read the explanation go the the next part in bold

Ok so the shorter leg of the triangle is a radius of the circle. ( This is indicated by the point in the middle of the circle.) for the hypotenuse we are given one part of the length (2) The other part also happens to be a radius ( remember that a radius is a line that starts from the center of the triangle to any point of the circumference. ) Also remember that the radius is equal to 3. That being said the hypotenuse = 2+3 which equals 5.

This triangle then happens to be a right triangle. ( A triangle formed by a tangent line and a radius is a right triangle.) This means that we can use the Pythagorean theorem to solve for x.

Below here is where the work is shown

a² + b² = c². where a and b = legs and c = hypotenuse. We are given the hypotenuse (5) and a leg (3) So we plug in what we are given and solve for the missing information. 5² = 3² + b²

5² = 25

3² = 9

we would then have 25 = 9 + b²

Next we subtract 9 from each side

25 - 9 = 16

9 - 9 cancels out

Now we have 16 = b²

finally we want to get rid of the ²

To do so we take the square root of each side

$\sqrt{16}=4\\\sqrt{b^2}=b\\b = 4$

we're left with b = 4 which means that x = 4

8 0

3 years ago

Find m<1 32 359 32° 35° Ob Od 90° 58°

Harrizon [31]

Answer:

d- m<1 = 58

Step-by-step explanation:

To find this answer we have to do multiple steps.

So we know that vertical angles are congruent by the definition of vertical angles, look at the picture

So, we also know that a triangle =180 degrees

therefore we can add 32 and 90 to find the 3rd angle measure

32+90=122, then 180(because that's the total of the triangle)-122=58

So, m<1=58 degrees

7 0

3 years ago