Answer:
The probability of a bulb lasting for between 480 and 526 hours=0.74454
Step-by-step explanation:
We are given that
Standard deviation of the lifetime,[tex]\sigma=20[/tex]hours
Mean, [tex]\mu=500[/tex]hours
We have to find the probability of a bulb lasting for between 480 and 526 hours.
[tex]P(480<x<526)=P(\frac{480-500}{20}<\frac{x-\mu}{\sigma}<\frac{526-500}{20})[/tex]
[tex]P(480<x<526)=P(-1<Z<1.3)[/tex]
[tex]P(480<x<526)=P(Z<1.3)-P(Z<-1)[/tex]
[tex]P(480<x<526)=0.90320-0.15866[/tex]
[tex]P(480<x<526)=0.74454[/tex]
Hence, the probability of a bulb lasting for between 480 and 526 hours=0.74454
