A student has submitted a concrete cylinder to the \"strength contest\" in Engin

Question

A student has submitted a concrete cylinder to the "strength contest" in Engineering Open House, and is scheduled to be the last contestant for load testing. The process producing her concrete cylinder yields strength that is normally distributed with mean = 80 kips and standard deviation = 20 kips (a kip is a non-SI unit of force). Immediately prior to her cylinder being tested, the two highest strengths in the contest thus far are 100 kips and 70 kips.

A. What is the probability that this student will be the second place winner?

B. Now the cylinder (from A) is being tested and it has not shown any kind of distress at a load of 90 kips. What is the probability that this student will win first place?

Please show all steps with a correct answer for a rating. Thanks in advance. :)

Explanation / Answer

mean = 80 kips and standard deviation = 20

A. What is the probability that this student will be the second place winner?

P(this student will be the second place winner ) = P(70kips < strength < 100 kips)

z-values corresponding to 70kips and 100 kips are:

z1 = (70-80)/20 = -0.5

z2 = (100-80)/20 = 1

required probability = P ( z1 < z < z2 ) = P( z < 1 ) - P ( z < -0.5 )

= 0.84134 - 0.30854 = 0.5328

B.

P(strength > 100 | strength is > 90) = P( 90 < strength < 100)/P(strength >90)

z-value corresponding to 100 kips = z2 = 1

z-value corresponding to 90 kips = z3 = (90-80)/20 =0.5

P( 90 < strength < 100) = P( z3 < z < z2) = P( z < 1) - P( z < 0.5) = 0.84134 - 0.69146 = 0.14988

P( strength > 90 ) = P ( z > z3) = 1 - P(z < 0.5) = 1 - 0.69146 = 0.30854

Required probability = 0.14988/0.30854 = 0.485772

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