Question

Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean value 14.0 kips and standard deviation 1.50 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 places.).

(b) P(X ≤ 17)

(c) P(X ≥ 6.5)

(d) P(13 ≤ X ≤ 16)

(e) P(|X − 14| ≤ 2)

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	14
std deviation   =σ=	1.5000

probability =

P(X<17)

=

P(Z<2)=

0.9772

b)

probability =

P(X>6.5)

=

P(Z>-5)=

1-P(Z<-5)=

1-0=

1.0000

c)

probability =

P(13<X<16)

=

P(-0.67<Z<1.33)=

0.9082-0.2514=

0.6568

d)

P(|X-14|<2) =P(-2+14 <X<2+14)=P(12<X<16)=P(-1.33 <Z<1.33)=0.9082-0.0918 =0.8164