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
klio [65]
3 years ago
11

An article suggested that yield strength (ksi) for A36 grade steel is normally distributed with μ = 42 and σ = 5.5.

Mathematics
1 answer:
alexandr1967 [171]3 years ago
8 0

Answer:

a)P( X

We want this probability:

P( X >64)

And using the z score formula given by:

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

We got:

P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316

b) For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=42 +0.674*5.5=45.707

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(42,25.5)  

Where \mu=42 and \sigma=5.5

And we want this probability:

P( X

And using the z score formula given by:

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

We got:

P( X

We want this probability:

P( X >64)

And using the z score formula given by:

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

We got:

P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316

Part b

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=42 +0.674*5.5=45.707

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.  

You might be interested in
What is the sum of 1.57 and 6.88?
CaHeK987 [17]

Answer:

The answer would be B: 8 ones, 4 tenths, and 5 hundredths.

Explanation:

First, you would have to use the equation: 1.57 + 6.88 = ?

Do the math, and 1.57 + 6.88 = 8.45

Now look at the answer choices. You can automatically get rid of every answer choice but B because none of them have an 8 in the ones place.

5 0
2 years ago
Read 2 more answers
Please Show the work
Svetradugi [14.3K]

the answer is a) because its the numerator is bigger than the denominator

8 0
3 years ago
ANYONE HELP ON THIS I HAVE 10 MINS LEFT ON MY FINAL PLEASE
igor_vitrenko [27]
It would be E) nothing, since it would be 289.82
6 0
2 years ago
If d= the number of dogs, which variable expression represents the phase below the sum of the number of dogs and the 6 cats
TEA [102]

although none of these are right, C would make the most sense

6 0
3 years ago
Read 2 more answers
Factor the polynomial function.<br> G(v) - 196v² + 100
miskamm [114]

Answer:

4(49v²+25)

Step-by-step explanation:

196 {v}^{2}  + 100

4(49 {v}^{2}  + 25)

3 0
2 years ago
Other questions:
  • 5 is 5% of what number w
    11·2 answers
  • What is the following is the solution to the equation 25^(z+2) = 125
    7·1 answer
  • What is the answer to this question 4(5x+30)=100?
    13·1 answer
  • A bagback that normally sales $39 is on sale for 30% off.Find the amount of the sale price
    9·1 answer
  • There are 10 fish, 5 of them drown &amp; 3 of them come back to life, how many are left?
    9·1 answer
  • Which expression can be used to find the volume of the sphere?
    12·2 answers
  • 3+3+3+3+3+3+3+333333
    12·2 answers
  • Hi can you please help me with my work
    11·1 answer
  • The prices of commodities X,Y,Z are respectively x, y, z, rupees per unit. Mr. A purchases 4 units of Z and sells 3 units of X a
    12·1 answer
  • John buys 3 pounds of cherries and 2 pounds of bananas he pays a total of $24.95 the bananas cost $6.50 less per pound than the
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!