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
Serhud [2]
3 years ago
9

The article "Monte Carlo Simulation—Tool for Better Understanding of LRFD" (J. Structural Engr., 1993: 1586–1599) suggests that

yield strength (ksi) for A36 grade steel is normally distributed with 43 and 4.5. a. What is the probability that yield strength is at most 40? Greater than 60? b. What yield strength value separates the strongest 75% from the others?
Mathematics
1 answer:
Sedaia [141]3 years ago
8 0

Answer:

a) P(X

And we can find this probability using the normal standard distribution or excel and we got:

P(z

b) P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

P(z>3.78)=1-P(Z

c) z=0.674

And if we solve for a we got

a=43 +0.674*4.5=46.033

So the value of height that separates the bottom 75% of data from the top 25% is 46.033.  

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".  

Solution to the problem

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(43,4.5)  

Where \mu=43 and \sigma=4.5

Part a

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

P(X

And we can find this probability using the normal standard distribution or excel and we got:

P(z

Part b

P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

P(z>3.78)=1-P(Z

Part c

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=43 +0.674*4.5=46.033

So the value of height that separates the bottom 75% of data from the top 25% is 46.033.  

You might be interested in
Find the sum of the first 50 terms.<br> 10-2/11n
Alexus [3.1K]

Answer:

in picture

yw :D

6 0
2 years ago
What is the value of the expression 5(X+3) when X=-3?
SIZIF [17.4K]

Answer:

0

Step-by-step explanation:

5(x+3) replace x with -3

5(-3+3)

5(0)

0

4 0
2 years ago
Hi I also need help with this please and thank you
OverLord2011 [107]

Answer:

Step-by-step explanation:

y=mx+b where m=slope and b=y intercept

m=(y2-y1)/(x2-x1)

m=(-2-4)/(2+1)

m=-2 so far we have the slope

y=-2x+b, using point (2,-2) we can solve for b, the y intercept

-2=-2(2)+b

-2=-4+b

2=b so we have our line

y=-2x+2, slope is -2 and y intercept is 2

8 0
3 years ago
Based on the graph, which inequality is correct for a number that is to the right of -4
Anon25 [30]

2 > -4

2 is greater than -4

3 0
3 years ago
HELP ME ASAP LAST PROBLEM
igomit [66]
The rate of change is -2 :)

5 0
3 years ago
Read 2 more answers
Other questions:
  • Susan buys a used car for $6,500 And finances it by making monthly payments of $325. How long will it take her to pay for the ca
    12·1 answer
  • Please help and show work thank you.
    11·2 answers
  • During his presidency from 1969 to 1974, Richard Nixon vetoed 43 congressional bills. Out of those vetoes, 7 were
    14·1 answer
  • What is the vertex of the quadratic equation y = - 1/3 (x + 2)^2 +5
    15·1 answer
  • Find the product. (-4·3·2)2 -48 48 -576 576
    11·2 answers
  • Which expression should be used to estimate the answer to this story problem? Marcus is reading a long novel. For 5 nights, he r
    14·2 answers
  • PLEASE WHOEVER ANSWERS ALL OF THEM GETS 80 POINTS AND BRAINLIEST
    13·1 answer
  • What is the coefficient of the third term in the binomial expansion of (a + b)6? 1 15 20 90
    11·2 answers
  • Someone please help me, write a variable equation to represent the situation, and solve it by using inverse operations.
    8·1 answer
  • How many solutions does the system of equations graphed below have?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!