Question

The probability that a life bulb will have a life time of more than 682 hours is 0.9788. The probability that a bulb will have a life time of more than 703 hours is 0.0051. Find the probability that a bulb will last for more than 648 hours.

Answer 1

$P(Z>z_1)=0.9788 \to P(Z<z_z)=1-0.9788 =0.0212 \to z_1=-2.03.$

$\frac{682-\mu}{\sigma}=-2.03 \to \mu-2.03\sigma=682.$

$P(Z>z_2)=0.0051 \to P(Z<z_2)=1-0.0051=0.9949 \to z_2=2.57.$

$\frac{703-\mu}{\sigma}=2.57 \to \mu+2.57\sigma=703.$

So, $(2.57+2.03)\sigma=703-682 \to \sigma=\frac{21}{4.6}=4.57.$

$\mu=682+2.03*4.57=691.$

$P(X>648)=P(Z>\frac{648-691}{4.57})=P(Z>-9.41)=1.$