The life in hours of a 75 watt light bulb is known to be normally distributed wi
ID: 3022798 • Letter: T
Question
The life in hours of a 75 watt light bulb is known to be normally distributed with theta= 25 hours. A random sample of 20 bulbs has a mean life of xbar = 1014 hours.B) construct a 99% two sided confidence interval on the mean life. D) construct a 99% lower-confidence bound on the mean life. ENGR 3800 Quality Control for Engineers Class Problems 4 1. The life in hours of a 75-watt light bulb is known to be normally distributed with -25 hours. A random sample of 20 bulbs has a mean life of 1014 hours. (a) Construct a 95% two-sided confidence interval on the mean life. (b) Construct a 99% two-sided confidence interval on the mean life. (c) Construct a 95% lower-confidence bound on the mean life. (d) Construct a 99% lower-confidence bound on the mean life. b)(x (1.evs). (1014-11 ,4 s)25.): (jalu-Mgsz)
Explanation / Answer
B)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 1014
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 25
n = sample size = 20
Thus,
Margin of Error E = 14.39932355
Lower bound = 999.6006764
Upper bound = 1028.399324
Thus, the confidence interval is
( 999.6006764 , 1028.399324 ) [ANSWER]
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d)
Note that
Lower Bound = X - z(alpha) * s / sqrt(n)
where
alpha = 1 - confidence level = 0.01
X = sample mean = 1014
z(alpha) = critical z for the confidence interval = 2.326347874
s = sample standard deviation = 25
n = sample size = 20
Thus,
Lower bound = 1000.99532
Thus, the confidence interval is
u > 1000.99532 [ANSWER]
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