The compressive strength of concrete is normally distributed with ? = 2500 psi and ? =...

The compressive strength of concrete is normally distributed with ? = 2500 psi and ? = 50 psi. Find the probability that a random sample of n = 10 specimens will have a sample mean diameter that falls in the interval from 2499 psi to 2610 psi.

Solutions

Expert Solution

Solution:

Given that,

= 2500

= 50

n = 10

So,

= 2500

= ( / $\sqrt$ n) = (50 / $\sqrt$ 10 ) = 15.8114) p

(2499 < < 2610 )

= p( 2499 - 2500 / 15.8114 ) ( - / ) < ( 2610 - 2500 / 15.8114)

= p ( - 1/15.8114 < z < 110 /15.8114 )

= p ( - 0.06 < z < 6.97)

= p (z < 6.97 ) - p ( z < - 0.06 )

Using z table

= 1 - 0.4761

= 0.5239

Probability = 0.5239

orchestra answered 1 year ago

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