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
Draw a box and whiskers plot of the numbers 7,4,7,5,5,3,7,6,7
wariber [46]

Answer

3,4,5,5,6,7,7,7,7

Step-by-step explanation:

5 0
2 years ago
20 POINTS)
olga_2 [115]

Answer:

D) 1,2

Step-by-step explanation:

Zeroes of a function are the x-values where y= 0

5 0
3 years ago
Will pick brainliest! I need help with this, actual effort in answering is much appreciated.
cupoosta [38]

Answer:

option 2

Step-by-step explanation:

4^2=16/8=2.  4^2=16/16=1.  2-1=1

3 0
2 years ago
Soccer balls go on sale for $7.50 each. The store also sells footballs and the manager wants to earn a daily profit of $400 from
Tasya [4]
At $7.50 per soccer ball, they earn a daily profit of $232.50.
The store needs to earn a daily profit of $400 – $232.50 = $167.50 from footballs.
Solve 167.50 = –4x2 + 80x – 150 to find the price for footballs: x = $5.46 and $14.54.
5 0
2 years ago
Read 2 more answers
To make one pack of cookies you need 34 cup of butter. How much butter is needed to make 4 1 / 2 pack of cookies?
stellarik [79]

Answer:

153 cups of butter

Step-by-step explanation:

1 pack=34 cups

1 pack(4.5 packs)=34 cups(4.5)

4.5 packs=153 cups of butter

5 0
3 years ago
Other questions:
  • Dave loves under water diving. His house boat is 250 feet above sea level. He jumped from that level. He went 600 feet below sea
    13·2 answers
  • from 2002 to 2012, the number of a particular make of cars sold at a dealership yearly declined to 500. The number is expected t
    14·1 answer
  • Will someone please help me with this problem!! **It's multiple choice!
    10·2 answers
  • What is the surface area of this
    8·2 answers
  • You sellBoth cookies and bread at a farmer’s market every Sunday you sell cookies go $5 a dozen and the bread for $4 a loaf your
    14·1 answer
  • Find the unpaid balance on the debt after 5 years of monthly payments on $190,000 at 3% for 25 years
    6·1 answer
  • after eating at the restaurant, jason, sandy, and sam decided to divide the bill evenly. if each person pid 34 dollars, what was
    7·1 answer
  • Simplify this polynomial identity 5(3+6)+2(7+3)
    14·1 answer
  • What is 73 square inches. What is the paper's area in square centimeters?
    6·1 answer
  • The price of a toaster increase 10% to $40. What is the original price of the toaster before the increase?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!