Question

The compressive strength of samples of cement can be modeled by a normal distribution with a mean of 6000 kilograms per square centimeter(Kg/cm2 ) and a variance of 10000.

1) What is the probability that a sample’s strength is less than 6250Kg/cm2 ?

2) What is the probability that a samples strength is between 5800 and 5900Kg/cm2?

3) What strength is exceeded by 95% of the samples?

Answer 1

The compressive strength of samples of cement can be modeled by a normal distribution with a mean of 6000 kilograms per square centimeter(Kg/cm2 ) and a variance of 10000.

1) What is the probability that a sample’s strength is less than 6250Kg/cm2 ?

Z value for 6250, z = (6250-6000)/sqrt(10000) =2.5

P( x <6250) = P( z < 2.5)

=0.9938

2) What is the probability that a samples strength is between 5800 and 5900Kg/cm2?

Z value for 5800, z = (5800-6000)/sqrt(10000) =-2

Z value for 5900, z = (5900-6000)/sqrt(10000) =-1

P( 5800<x<5900) = P( -2<z<-1)

=P( z < -1) –P( z < -2) =0.1587-0.0228

=0.1359

3) What strength is exceeded by 95% of the samples?

Z value for top 95% = -1.645

Sd= sqrt(10000) =100

X= mean+z*sd = 6000-1.645*100

=5835.5