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 lifetime of ; 1. At least 300 hours
2. At least 100 hours
3. Between 150 and 250 hours

Answer 1

$Given \; that, μ=210, σ=56, then,\\ 1)P(x>300)=P(Z>\frac{300-210}{56})\\ =P(Z>1.61)=0.5-P(0<Z<1.61)\\ =0.5-0.4463=0.0537\\ 2) P(x>100)=P(Z>\frac{100-210}{56})\\ =P(Z>-1.96)\\=0.5+P(0<Z<1.96)\\ =0.5+0.4750=0.9750\\ 3)P(150<x<250)\\ =P(\frac{150-210}{56}<Z<\frac{250-210}{56})\\ =P(-1.07<Z<0.71)\\ =P(0<Z<1.07)+P(0<Z<0.71)\\ =0.3577+0.2611=0.6188\\$