Suppose the force acting on a column that helps to support a building is a norma

Question

Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean value 12.0 kips and standard deviation 1.25 kips. Compute the following probabilities by standardizing and then using a standard normal curve table from the Appendix Tables. (Round your answers to four decimal P (X lessthanorequalto 12) P (X lessthanorequalto 14.5) P (X greaterthanorequalto 5.75) P (11 lessthanorequalto X lessthanorequalto 15) P (| X-12 | lessthanorequalto 1)

Explanation / Answer

from normal distribution zscore =(X-mean)/std deviation

a)P(X<12) =P(Z<0) =0.5

b)P(X<14.5)=P(Z<2)=0.9772

c)P(X>5.75)=1-P(Z<-5)=1-0.0000=1

d)P(11<X<15)=P(-0.8<Z<2.4)=0.9918-0.2119=0.7799

e)P(|x-12|<1) =P(11<X<13) =P(-0.8<Z<0.8)=0.7881-0.2119=0.5763

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