Answer:
Step-by-step explanation:
Using normal distribution,
z = (x - μ)/σ
μ= mean = 44 and
σ = standard deviation= 5.0
a) The probability that yield strength is at most 40=
P( x lesser than or equal to 40)
z = (40-44)/5= -0.8
Looking at the normal distribution table,
P( x lesser than or equal to 40) =0.2119
b) P(x greater than 62) = 1 - P(x lesser than or equal to 62)
z = (62-44)/5= 3.6
Looking at the normal distribution table,
P(x greater than 62) = 1 -0.99984
= 0.00016
c)P( 42 lesser than or equal to x lesser than or equal to 62)
= P(x lesser than or equal to 62) - P( x lesser than or equal to 40)
= 0.99987-0.2119= 0.78797
d) What yield strength value separates the strongest 75% from the others.
To get x for strongest 75, we get the z value corresponding to 0.75 from the table
z = 0.675= (x-44)/5
x = 3.375+44 = 47.375
The rest is 25% = 0.25
we get the z value corresponding to 0.25 from the table)
z = -0.67 = (x-44)/5
-3.35= x -44
x = -44+3.35= 40.65
yield strength value that separates the strongest 75% from the others
=47.375-40.65= 6.725
The probability that the yield strength is at most 40 is approximately 0.2119 and the probability that it is greater than 62 is approximately 0.0001. The yield strength value that separates the strongest 75% from the others is approximately 40.628 ksi.
This question is about calculating probabilities and percentiles using the properties of the normal distribution. The yield strength for the A36 grade steel is normally distributed with a mean (μ) of 44 and a standard deviation (σ) of 5.0.
(a) To find the probability that the yield strength is at most 40, we will need to calculate the Z-score value for the yield strength of 40. The Z-score can be calculated using the following formula: Z = (X - μ) / σ , where X is the observed value, μ is the mean, and σ is the standard deviation. For X = 40, μ = 44, and σ = 5.0, the Z-score is -0.8. Looking up the Z-score in the standard normal distribution table, the probability that the yield strength is at most 40 is approximately 0.2119. Using a similar process, we find that the probability that the yield strength is greater than 62 is less than 0.0001, very close to zero.
(b) To determine the yield strength value that separates the strongest 75% from the others, we find the Z-score that corresponds to a cumulative probability of 0.25 in the standard normal distribution table (because the strongest 75% corresponds to the weakest 25%). That Z-score is approximately -0.6745. Using the formula Z = (X - μ) / σ to solve for X gives us X = σZ + μ = 5.0 * -0.6745 + 44 = 40.6275, which rounded to three decimal places is 40.628.
#SPJ3
P(Larger or blue) = 7/10. In a bag we have blue and red marbels, which are large and small as in the table shown in the image, the probability of taking a large or blue marble is 7/10.
The key to solve this problem is find the probability of the union events using the equation P(A∪B) = P(A) + P(B) - P(A∩B).
For this problem we have P(Large or Blue) = P(Large) + P(Blue) - P(Large and Blue). The total of the large ones is 25 and the small ones is 15, meaning that the sum of both is 40. P(large) = 25/40, P(Blue) 20/40, and P(Large and Blue) = 17/40
P(Large or Blue) = 25/40 + 20/40 - 17/40 = 28/40 dividing by 4 both terms of the fraction.
P(large or Blue) = 7/10
a) 841
b) 106
c) 3 051
To illustrate numbers using base 10 blocks, you need to understand the place values and represent each digit using the appropriate base 10 block.
To illustrate numbers using base 10 blocks, we need to understand that each number is made up of different place values—ones, tens, hundreds, and so on. A base 10 block for the number 841 would consist of 8 hundreds blocks, 4 tens blocks, and 1 ones block. For the number 106, we would have 1 hundreds block, 0 tens blocks, and 6 ones blocks. Lastly, for the number 3,051, we would have 3 thousands blocks, 0 hundreds blocks, 5 tens blocks, and 1 ones block.
x/y+17
If is x=12
and y=1/2
Answer:
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-x-2y=8
A. (8,7)
B. No solution
C. (-7,8)
D. (-8,7)
If you can, please explain step by step:)
Answer: D
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
thats the answer ^^
Answer:
its the second one
Select all numbers that are in the domain.
Answer:
-3 -3 -1 1
Step-by-step explanation:
give me five stars and ill tell you
Answer: Answer: -3,-1, and 1.
Step-by-step explanation: You are given the relation R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} The domain of the relation are all possible inputs and the range of the relation are all possible outputs. So, the inputs are : -3,-1,1; and the outputs are : -2,0,2. As a result, the domain is : -3,-1,1; and the range is : -2,0,2.