Read It to a 8. O -3 points DevoreStat9 4 E.040 An article suggested that yield

Question

Read It to a 8. O -3 points DevoreStat9 4 E.040 An article suggested that yield strength (ksi) for A36 grade steel is normally distributed with ? = 43 and ? = 5.5. (a) What is the probability that yield strength is at most 407 Greater than 647 (Round your answers to four decimal places.) at most 40 greater than 64 | b whatyield strength value separates the strong est 75% from the others? (Round your answer to three decimal places.) ksi You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? DELL

Explanation / Answer

P(X < A) = P(Z < (A - mean)/standard deviation)

(a) P(at most 40) = P(X < 40)

= P(Z < (40 - 43)/5.5)

= P(Z < 0.545)

= 0.7071

P(X > 64) = 1 - P(X < 64)

= 1 - P(Z < (64 - 43)5.5)

= 1 - P(Z < 3.82)

= 1 - 0.9999

= 0.0001

(b) Let A be the yield strength that represent the strongest 75%

P(X > A) = 0.75

P(X < A) = 0.25

P(Z < (A - 43)/5.5) = 0.25

From standard normal distribution table,

(A - 43)/5.5) = -0.67

A = 39.315 ksi

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