The breaking strength of steel bars from a certain distributor is normally distr

Question

The breaking strength of steel bars from a certain distributor is normally distributed with a mean of 235 pounds per square inch and a standard deviation of 40. a) What is the probability that one randomly chosen steel bar from the #2) distributor will have a breaking strength in the range of 245 to 255 pounds per square inch ? b) Ace Construction is building a bridge and is required by code to use Class A steel bars in the construction. A load of steel bars will be accepted from this distributor if the mean breaking strength ofa random sample of thirty' steel bars is higher than 250 pounds per square inch. What is the probability that a shipment of steel bars received today will be accepted?

Explanation / Answer

mean is 235 and s is 40

z is given as (x-mean)/s

a) P(245<x<255)=P((245-235)/40<z<(255-235)/40)=P(0.25<z<0.5) or P(z<0.5)-P(z<0.25)

from normal distribution table we get 0.6915-0.5987=0.0928

b) P(x>250)=P(z>(250-235)/40)=P(z>0.38) or 1-P(z<0.38)=1-0.6480=0.352

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