Question

The life time of a certain brand of bulbs produced by a company is normally
distributed, with mean 210 hours and standard deviation 56 hours. What is the
probability that a bulb picked at random from this company’s products will
have a life time of:
(i) at least 300 hours,
(ii) at most 100 hours,
(iii) between 150 and 250 hours.

Answer 1

Let X be a random variable representing the lifetime of bulbs

X~N(210,56²)

$z=\frac {x-\mu}{\sigma}$

i) P(X>300)

$=\frac {300-210}{56}=1.607$

P(z>1.607) =0.054 from the standard normal tables

=0.054

ii) P(z<100)

=$\frac{100-210}{56}=-1.964$

P(Z<-1.964)=0.025 from the z tables

=0.025

iii) P(150<X<250)

$z_1=\frac{150-210}{56}=-1.071$

P(z<-1.071)=0.142

$z_2=\frac{250-210}{56}=0.714$

P(z<0.714)=0.762

=0.762-0.142

=0.620