Again this is my second time i am asking this question plsssss can you do the ri

Question

Again this is my second time i am asking this question plsssss can you do the right answer

Young s modulus ? qua ttative measure o stf ness o?n cost c matonal. Suppose that or metal chce s of ? paricular typo, its mean value and standard deviat on are 00 GPg and 1.9 GPa respective y Suppose the stri ution normal Round your answers to our deci mal piaces.] (a) Calculate 89 s X 1) when n- 25. b) Haw Ikely is it that the semple mean diameter exueeds 92 when -35 You may nesd to use the appropriste table in the Appendx of Tebles to answer this question.

Explanation / Answer

Given that the random variable X has :

mean = 90

sd = 1.9

n = 25

And we have to find P(80 < Xbar < 91)

We know that,

Xbar ~ N(mean = 90, sd = 1.9/sqrt(25) = 0.38)

COnvert Xbar = 80 and Xbar = 91 into z-scores.

z-score is defined as,

z = (Xbar - mean) / sd

z = (80 - 90) / 0.38 = -26.3

z = (91 - 90) / 0.38 = 2.6

Now we have to find P(-26.3 < Z < 2.6)

P(-26.3 < Z < 2.6)= P(Z < 2.6) - P(Z < -26.3)

By using statistical table,

P(-26.3 < Z < 2.6) = 0.9958 - 0.0000 = 0.9958

Now again we have to find P(Xbar > 91) when n = 36

Here standard deviation changes.

sd = 1.9 / sqrt(36) = 0.32

z = (91 - 90) / 0.32 = 3.16

Now we have to find P(Z>3.16)

P(Z > 3.16) = 0.0008

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