The quality control manager Ms Venkat at Mangal Light Ltd in

The quality control manager Ms. Venkat at Mangal Light Ltd, in Trinidad needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 100 hours. A random sample of 64 light bulbs indicated a mean of 350 hours.

Solution

a)
Note that              
              
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 =    0.025          
X = sample mean =    350          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    100          
n = sample size =    64          
              
Thus,              
              
Lower bound =    325.5004502          
Upper bound =    374.4995498          
              
Thus, the confidence interval is              
              
(   325.5004502   ,   374.4995498   )[ANSWER]

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B)

No, as 400 is not within the confidence interval.

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c)

NO, as by central limit theorem, the distirbution of means will be approximately normally distirbuted regardless of the underlying distribution.

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