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
irinina [24]
3 years ago
5

If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is Wit

hin 0.8 SDs of its mean value? Farther than 2.3 SDs from its mean value? Between 1 and 2 SDs from its mean value?
Mathematics
1 answer:
KatRina [158]3 years ago
4 0

Answer:

a) 0.5762

b) 0.0214

c) 0.2718

Step-by-step explanation:

It is given that lengths of the bolt thread are normally distributed. So in order to find the required probability we can use the concept of z distribution and z scores.

Part a) Probability that length is within 0.8 SDs of the mean

We have to calculate the probability that the length of a bolt thread is within 0.8 standard deviations of the mean. Recall that a z- score tells us that how many standard deviations away a value is from the mean. So, indirectly we are given the z-scores here.

Within 0.8 SDs of the mean, means from a score of -0.8  to +0.8. i.e. we have to calculate:

P(-0.8 < z < 0.8)

We can find these values from the z table.

P(-0.8 < z < 0.8) = P(z < 0.8) - P(z < -0.8)

= 0.7881 - 0.2119

= 0.5762

Thus, the probability that the thread length of a randomly selected bolt is within 0.8 SDs of its mean value is 0.5762

Part b) Probability that length is farther than 2.3 SDs from the mean

As mentioned in previous part, 2.3 SDs means a z-score of 2.3.

2.3 Standard Deviations farther from the mean, means the probability that z scores is lesser than - 2.3 or greater than 2.3

i.e. we have to calculate:

P(z < -2.3 or z > 2.3)

According to the symmetry rules of z-distribution:

P(z < -2.3 or z > 2.3) = 1 - P(-2.3 < z < 2.3)

We can calculate P(-2.3 < z < 2.3) from the z-table, which comes out to be 0.9786. So,

P(z < -2.3 or z > 2.3) = 1 - 0.9786

= 0.0214

Thus, the probability that a bolt length is 2.3 SDs farther from the mean is 0.0214

Part c) Probability that length is between 1 and 2 SDs from the mean value

Between 1 and 2 SDs from the mean value can occur both above the mean and below the mean.

For above the mean: between 1 and 2 SDs means between the z scores 1 and 2

For below the mean: between 1 and 2 SDs means between the z scores -2 and -1

i.e. we have to find:

P( 1 < z < 2) + P(-2 < z < -1)

According to the symmetry rules of z distribution:

P( 1 < z < 2) + P(-2 < z < -1) = 2P(1 < z < 2)

We can calculate P(1 < z < 2) from the z tables, which comes out to be: 0.1359

So,

P( 1 < z < 2) + P(-2 < z < -1) = 2 x 0.1359

= 0.2718

Thus, the probability that the bolt length is between 1 and 2 SDs from its mean value is 0.2718

You might be interested in
A boulder falls off the top of a cliff during a storm. The cliff is 90 feet high.
andreev551 [17]

Answer:

It will take the boulder approximately 4.28 seconds to hit the road

Step-by-step explanation:

The given height of the cliff from which the boulder falls, h = 90 feet

The equation that can be used to find the time it takes the boulder to fall is h = u·t + (1/2)·g·t²

Where;

h = The height of the cliff = 90 ft.

u = The initial velocity of the boulder = 0 m/s (The boulder is assumed to be at rest when it falls)

g - The acceleration due to gravity ≈ 9.81 m/s²

t = How long it will take for the boulder to hit the road below

Plugging in the values gives;

90 = 0 × t + (1/2)×9.81×t² = 4.905·t²

∴ t = √(90/4.905) ≈ 4.28

The time it takes the boulder to hit the road, t ≈ 4.28 seconds.

7 0
3 years ago
if u play ro-b-lox blox-burg, answer!! dont answer if u dont.. but is it fair if i say abc tk help me make snowmans and each sno
Papessa [141]

Answer:

You probably should have gave them 2/3 of what they did. I wouldn't call you a scammer, but it was not fair.

3 0
3 years ago
Circle the greater andend. draw circle to count on one two or three write the sum
Natali5045456 [20]
Um where the problem or number?
3 0
3 years ago
Given the function f(x) = 2x, find the value of f−1(32).
Oliga [24]

Answer:

it is -30

Step-by-step explanation:

you would divide both sides by x,then f=2

using PEMDAS we come to -30

5 0
3 years ago
Evaluate if a= 28 and b= -3 a/4+b
patriot [66]

Answer:

4

Step-by-step explanation:

divide the numbers


subtract the numbers


final answer:
= 4

8 0
2 years ago
Other questions:
  • Esther is participating in a walk-a-thon. She will raise 5 dollars for her charity for each lap she walks.
    10·2 answers
  • Book $22.50 markup percent 42% what is the markup and retail price.
    14·2 answers
  • Which equation best represents the line graphed above? <br><br><br> Please help
    8·1 answer
  • Assume f(x)=-2+8 and g(x)=3x what is the value of (f+g)(-1)
    11·1 answer
  • When is 149 dollars in Hondurans
    5·1 answer
  • HELP NEEDED ASAP I WILL GIVE BRAINLIEST TO WHOEVER GETS CORRECT
    12·2 answers
  • BRAINLIEST!!<br><br> QUICKK:<br><br> which is bigger Saturn or Jupiterrrrrr
    14·2 answers
  • What is the value of x in this proportion?
    9·2 answers
  • Find the next two terms in this sequence.<br><br> 4,8,-16,-32,64, [??],[??]
    8·1 answer
  • Find the surface area of the triangular prism.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!