Question

The life in hours of a 75-watt light bulb is known to be normally distributed with σ = 25 hours. a random sample of 20 bulbs has a mean life of x = 1014 hours. (a) construct a 99% two-sided confidence interval on the mean life. (b) construct a 99% lower-confidence bound on the mean life. compare the lower bound of this confidence interval with the one in part (a).

Answer 1

a] construct a 99% two-sided confidence interval on the mean life
The formula for confidence interval is given by:
μ+/-z(σ/√n)
thus we shall have:
z(0.995)
1014+/-2.58(25/√75)
=1014+/-7.448
=1021.448or 1006.552
Thus thus the answer is (1021.448,1006.552)

b] construct a 99% lower-confidence bound on the mean life.
Here we shall use the same formula but:
z-score will be:
z(0.99)=2.34
1014+/-2.34(25/√75)
=1014+/- 6.755
=1020.755 or 1007.245
the answer is (1020.755, 1007.245)