Suppose a brand of light bulbs is normally​ distributed, with a mean life of 1400 hr and a standard deviation of 150 hr. Find the probability that a light bulb of that brand lasts between 1175 hr and 1610 hr.

Answer:The probability that a light bulb of that brand lasts between 1175 hr and 1610 hr is 0.8524.Step-by-step explanation:Given : Suppose a brand of light bulbs is normally​ distributed, with a mean life of 1400 hr and a standard deviation of 150 hr. To find : The probability that a light bulb of that brand lasts between 1175 hr and 1610 hr ?Solution : Applying z-score formula,[tex]z=\frac{x-\mu}{\sigma}[/tex]where, [tex]\mu=1400[/tex] is population mean[tex]\sigma=150[/tex] is standard deviationFor x=1175 hour,[tex]z=\frac{1175-1400}{150}[/tex][tex]z=\frac{-225}{150}[/tex][tex]z=-1.5[/tex]For x=1610 hour,[tex]z=\frac{1610-1400}{150}[/tex][tex]z=\frac{210}{150}[/tex][tex]z=1.4[/tex]The required probability is, [tex]P(1175< X<1610)=P(-1.5<z<1.4)[/tex][tex]P(1175< X<1610)=P(z<1.4)-P(z<-1.5)[/tex] Using z table, the values are[tex]P(1175< X<1610)=0.9192-0.0668[/tex][tex]P(1175< X<1610)=0.8524[/tex]The probability that a light bulb of that brand lasts between 1175 hr and 1610 hr is 0.8524.