Question

2. The florescent lights in a classroom function for an exponential amount of time with mean 1,200 hours.

a. What is the probability a light functions for at least 1,500 hours?

b. What is the probability a light functions for at least 2,500 hours, given that it has already operated for 1,000 hours?

c. Find a 95% confidence interval for hours a light will last.

Answer 1

here parameter =1200

a) probability a light functions for at least 1,500 hours =P(X>1500)=e^-x/ =e^-1500/1200 =0.2865

b)

probability a light functions for at least 2,500 hours, given that it has already operated for 1,000 hours

=P(X>2500|X>1000) =P(X>2500-1000)=P(X>1500)=e^-x/ =e^-1500/1200 =0.2865

c)

fpr 95% middle values falls between 2.5 and 97.5 th percentile ;

2.5 th percentile =-*ln(1-p)=-1200*ln(0.975)=30.38

and 97.5 th percentile =-*ln(1-p)=-1200*ln(0.025)=4426.66

hence 95% confidence interval for hours a light will last =30.38 to 4426.66