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
dem82 [27]
3 years ago
7

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.725.72 millimeters and a standard de

viation of 0.070.07 millimeters. Find the two diameters that separate the top 5%5% and the bottom 5%5%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.
Mathematics
2 answers:
suter [353]3 years ago
7 0

Answer:

Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 5.72, \sigma = 0.07

Top 5%:

X when Z has a pvalue of 0.95. So X when Z = 1.645

Z = \frac{X - \mu}{\sigma}

1.645 = \frac{X - 5.72}{0.07}

X - 5.72 = 1.645*0.07

X = 5.84

Bottom 5%:

X when Z has a pvalue of 0.05. So X when Z = -1.645

Z = \frac{X - \mu}{\sigma}

-1.645 = \frac{X - 5.72}{0.07}

X - 5.72 = -1.645*0.07

X = 5.60

Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.

lozanna [386]3 years ago
4 0

Answer:

The two diameters that separate the top 5% and the bottom 5% are 5.84 and 5.60 respectively.

Step-by-step explanation:

We are given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.72 millimeters and a standard deviation of 0.07 millimeters.

<em>Let X = diameters of bolts produced in a machine shop</em>

So, X ~ N(\mu=5.72,\sigma^{2} = 0.07^{2})

The z score probability distribution is given by;

         Z = \frac{X-\mu}{\sigma} ~ N(0,1)

where, \mu = mean diameter = 5.72 millimeter

            \sigma = standard deviation = 0.07 millimeter

<u>Now, we have to find the two diameters that separate the top 5% and the bottom 5%.</u>

  • Firstly, Probability that the diameter separate the top 5% is given by;

       P(X > x) = 0.05

       P( \frac{X-\mu}{\sigma} > \frac{x-5.72}{0.07} ) = 0.05

       P(Z > \frac{x-5.72}{0.07} ) = 0.05

<em>So, the critical value of x in z table which separate the top 5% is given as 1.6449, which means;</em>

                 \frac{x-5.72}{0.07}  = 1.6449

               {x-5.72} = 1.6449 \times {0.07}

                        x   = 5.72 + 0.115143 = <u>5.84</u>

  • Secondly, Probability that the diameter separate the bottom 5% is given by;

       P(X < x) = 0.05

       P( \frac{X-\mu}{\sigma} < \frac{x-5.72}{0.07} ) = 0.05

       P(Z < \frac{x-5.72}{0.07} ) = 0.05

<em>So, the critical value of x in z table which separate the bottom 5% is given as -1.6449, which means;</em>

                 \frac{x-5.72}{0.07}  = -1.6449

               {x-5.72} = -1.6449 \times {0.07}

                        x   = 5.72 - 0.115143 = <u>5.60</u>

Therefore, the two diameters that separate the top 5% and the bottom 5% are 5.84 and 5.60 respectively.

You might be interested in
In the graphic below, if W and X are right angles and WY = XY
elena-14-01-66 [18.8K]
Answer is HL

YZ = YZ
WY = XY

<X and <W is right angle

<span>if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent</span>
7 0
3 years ago
I don't know how to explain it but please help!
Wittaler [7]

Answer:

required answer. is 1/x³

7 0
3 years ago
Simplify to create an equivalent expression.<br> 8(a+2)+2(2+3a)=
Alchen [17]

Answer:

14a + 20

Step-by-step explanation:

8(a + 2) + 2(2 + 3a)

expand the bracket

8a + (8*2) + (2*2) + (2*3a)

8a + 16 + 4 + 6a

bring like terms together

8a + 6a + 16 + 4

14a + 20

3 0
3 years ago
Romeo had pound of fudge left. He divided the remaining fudge into -pound 5 16 bags. Write and solve an equation that models the
lbvjy [14]

Answer:

3/4     /     5/16

Step-by-step explanation:

3/4     /     5/16   =  15/2 pound bags

8 0
2 years ago
Plz answer this correctly to get more points
crimeas [40]

Answer: x = 30°

Concept:

Here, we need to know the idea of an isosceles triangle and the vertical angle theorem.

An <u>isosceles triangle</u> is a triangle that has any two of its sides equal to each other. Also, the angles opposite these equal sides are equal, which is basically the base angles.

The <u>vertical angle theorem</u> states that two vertical angles formed when two lines intersect each other are always equal to each other.

Solve:

<u>Find the other base angle of the isosceles triangle.</u>

Since there are two equal sides, we know that this is an isosceles triangle.

Since the definition said that the base angles are equal, the other base angle would also be x.

<u>Find the value of x</u>

According to the vertical angle theorem, two vertical angles formed by intersection are equal.

Just as angle x and 30°, are vertical angles formed by intersection, therefore, \boxed{x=30}

Hope this helps!! :)

Please let me know if you have any questions

8 0
3 years ago
Other questions:
  • 11 times a number increased by 2 is the same as 6 more than 9 times the number .Find the number.
    8·1 answer
  • Anna baked <br> 3 batches of cookies with <br> c cookies in each batch. She then ate <br> 8 cookies!
    6·2 answers
  • The odometer of a new automobile functions improperly and registers only 2 miles for every 3 miles driven. If the odometer indic
    5·1 answer
  • 15DANCE TICKETS WERE SOLD IN ONE HALF HOUR. IF THIS RATE CONTINUES HOW LONG WOULD YOU EXPECT IT TO TAKE TO SELL 270 tickets.
    7·1 answer
  • Which shows 542 − 462 being evaluated using the difference of squares method?
    15·2 answers
  • If the point (2/3,y) is on the unit circle, what is y?
    7·1 answer
  • One book costs £2.98. how much do 4 books cost?
    7·1 answer
  • Find the slope of the line that passes through the pair of points.<br> (1,-4), (-5, -3)
    10·2 answers
  • PLEASE HURRY!!! <br> select all angles are congruent to 10.
    5·2 answers
  • What is the product? 1/2• [12 64 78 30]
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!