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mr Goodwill [35]
3 years ago
8

g The tensile 0.2 percent offset yield strength of AISI 1137 cold-drawn steel bars up to 1 inch in diameter from 2 mills and 25

heats is reported as follows: S y 93 95 97 99 101 103 105 107 109 111 f 19 25 38 17 12 10 5 4 4 2 where y S is the class midpoint in kpsi and f is the number in each class. Presuming the distribution is normal, what is the yield strength exceeded by 99 percent of the population
Mathematics
1 answer:
Vitek1552 [10]3 years ago
3 0

Answer:

107.50

Step-by-step explanation:

Given the following :

Midpoint (S)____F

S y 93 95 97 99 101 103 105 107 109 111 f 19 25 38 17 12 10 5 4 4 2

Calculating the mean and standard deviation using a calculator :

The mean(m) of the data above = 98.12

Standard deviation (sd) = 4.02

Proportion = 99% of population

From z table = 2.33

Using :

Zscore =(x - m) / sd

2.33 = (x - 98.12) / 4.02

2.33 * 4.02 = x - 98.12

9.3666 = x - 98.12

9.3666 + 98.12= x

x = 107.4866

X = 107.50

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Piecewise Function is like multiple functions with a speific/given domain in one set, or three in one for easier understanding, perhaps.

To evaluate the function, we have to check which value to evalue and which domain is fit or perfect for the three functions.

Since we want to evaluate x = -8 and x = 4. That means x^2 cannot be used because the given domain is less than -8 and 4. For the cube root of x, the domain is given from -8 to 1. That meand we can substitute x = -8 in the cube root function because the cube root contains -8 in domain but can't substitute x = 4 in since it doesn't contain 4 in domain.

Last is the constant function where x ≥ 1. We can substitute x = 4 because it is contained in domain.

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The nth root of a can contain negative number only if n is an odd number.

\large{  \begin{cases} f( - 8 ) =   \sqrt[3]{ - 2 \times -  2 \times   - 2}  \\ f(4) = 3 \end{cases}} \\  \large{  \begin{cases} f( - 8 ) =  - 2\\ f(4) = 3 \end{cases}}

Answer

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