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NikAS [45]
3 years ago
13

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviat

ion of 0.08 millimeters. Find the two diameters that separate the top 4% and the bottom 4%. These diameters could serve as limits used to identify which bolts should be rejected
Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
7 0

Answer:

The bolts with diameter less than 5.57 millimeters and with diameter greater than 5.85 millimeters should be rejected.

Step-by-step explanation:

We have been given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviation of 0.08 millimeters.    

Let us find the sample score that corresponds to z-score of bottom 4%.  

From normal distribution table we got z-score corresponding to bottom 4% is -1.75 and z-score corresponding to top 4% or data above 96% is 1.75.

Upon substituting these values in z-score formula we will get our sample scores (x) as:

z=\frac{x-\mu}{\sigma}

-1.75=\frac{x-5.71}{0.08}

-1.75*0.08=x-5.71

-0.14=x-5.71

-0.14+5.71=x-5.71+5.71

5.57=x

Therefore, the bolts with diameters less than 5.57 millimeters should be rejected.

Now let us find sample score corresponding to z-score of 1.75 as upper limit.

1.75=\frac{x-5.71}{0.08}

1.75*0.08=x-5.71

0.14=x-5.71

0.14+5.71=x-5.71+5.71

5.85=x  

Therefore, the bolts with diameters greater than 5.85 millimeters should be rejected.

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The frequency table shows the favorite college football teams of middle school students.What fraction of the students chose soon
masya89 [10]
The fraction would be 5/20=1/4=.25 in decimal form.

4 0
3 years ago
Read 2 more answers
Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the f
Molodets [167]

Answer:

b. type II

Step-by-step explanation:

given that food inspectors  inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses.

H0: the food is safe

Ha: the food is not safe

It was concluded from the hypothesis test that the food is safe while it was not actually safe.

This is a case of false acceptance of null hypothesis when it is false.

In hypothesis test, there are two errors. a type I error is the rejection of a true null hypothesis  while a type II error is the non-rejection of a false null hypothesis

So this is type II error because we did not reject a false null hypothesis.

8 0
3 years ago
Can you help me pleeeeaaassee??
melamori03 [73]

Error 1: DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC, Error 2: The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1), Error 3:The third error is the value of x and we can find the correct value of x from the equation 14 / 7 = 16 / (x - 1) and the value of x is 9.

Given: The diagram is given and we need to find the errors and then fix them. Also ΔTSR ≈ ΔTCD

Let's solve the given question:

Given that ΔTSR ≈ ΔTCD

So we know by the properties of the similarity that if two triangles are similar then the ratio of their corresponding sides is equal.

So, ΔTSR ≈ ΔTCD

=> RT / TD = ST / TC

=> 14 / 7 = 16 / (x - 1)

In the question, we can observe that the given side ratio is DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC.

The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1).

The third error is the value of x.

We can find the correct value of x from the given equation:

14 / 7 = 16 / (x - 1)

=> 2 = 16 / (x - 1)

Multiplying both sides by (x - 1):

(x - 1) × 2 = 16 / (x - 1) × (x - 1)

=> 2(x - 1) = 16

Multiplying both sides by 1 / 2:

2(x - 1) × 1 / 2= 16 × 1 / 2

=> x - 1 = 8

Adding 1 on both sides:

x - 1 + 1 = 8 + 1

x = 9

Therefore x = 9.

Hence the errors are:

Error 1: DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC

Error 2: The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1).

Error 3:The third error is the value of x and we can find the correct value of x from the equation 14 / 7 = 16 / (x - 1) and the value of x is 9.

Know more about "similar triangles" here: brainly.com/question/14366937

#SPJ9

8 0
1 year ago
A backyard pool has a concrete walkway around it that is 3 feet wide on all sides. The total area of the pool and the walkway is
Gnoma [55]

Answer:

<h2><em>29.4 length and 21.4 width.</em></h2>

Step-by-step explanation:

To fin the dimensions of the pool we need to use the total area of the pool plus the concrete walkway. Lets say that <em>W </em>is the width and <em>L </em>the length. We know that, the walkway has 3 ft wide, this means that the width and length are increased by 6ft (3ft on each side). So, the total area can be expressed like this:  A_{total} = (L+6)(W+6).

In addition, we know that the total area is 970 and the length is 8 ft longer than the width (L=W+8). So:

A_{total} = (L+6)(W+6)\\970 = (W+8+6)(W+6)\\970=W^{2}+20W+84\\W^{2}+20W-886=0

With this quadratic equation we're gonna have to solution, the most reasonable is part of the answer. So, solving the equation we have as solutions: W_{1}=21.4 and  W_{2}=-41.4

Therefore, the width is 21.4 ft, because the negative number cannot represent distances.

Using the relation between length and width:

L=W+8\\L=21.4+8=29.4

<em>Therefore, the dimensions of the pool are 29.4 length and 21.4 width.</em>

7 0
3 years ago
Please solve the problem.
Deffense [45]
OK.  I did it, and I have the solution.
_____________________________________

The length of the deck is  (5 + 2x) .
The width of the deck is   (4 + 2x) .

If the deck didn't have that big hole in the middle where the pool is,
then its area would be

                 (5 + 2x) · (4 + 2x) .

When you multiply that all out, you get    Area = 4x² + 18x + 20

and the question tells us that the area of the whole big rectangle is 90 yds² .
So we can write

                                             4x² + 18x + 20  =  90 .

Subtract 90 from each side:    4x² + 18x - 70  =  0
Divide each side by 2 :           2x² + 9x - 35  =  0

You can use the quadratic equation to solve that and find out that
x = 2.5 yards, and that's what the question is asking you.
___________________________________________________

That makes the deck  10 yds high and 9 yds wide.

Total area of the whole big rectangle, (deck + pool ),  =  90 yds².
 
3 0
3 years ago
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