A random sample of 56 fluorescent light bulbs has a mean life of 645 hours. Assume the population standard deviation is 31 hours. Construct a 95% confidence interval for the population mean.
A)(636.9, 653.1)
B)(539.6, 551.2)
C)(112.0, 118.9)
D)(712.0, 768.0)

Question

Quizplus · Accepted Answer

To construct a confidence interval for the population mean, we will use the formula:

CI = X̄ ± Z* (σ/√n)

Where:
X̄ = sample mean = 645
Z* = critical value for a 95% confidence interval = 1.96
σ = population standard deviation = 31
n = sample size = 56

Plugging in the values, we get:

CI = 645 ± 1.96 * (31 / √56)

Simplifying, we get:

CI = 645 ± 7.05

So the 95% confidence interval for the population mean is:

(645 - 7.05, 645 + 7.05) = (636.9, 653.1)

Therefore, the best choice is A) (636.9, 653.1). Since we are dealing with a sample mean and a known population standard deviation, we can use a z-distribution to construct our confidence interval. We use the formula:
CI = X̄ ± z*(σ/√n)
where X̄ is the sample mean, σ is the population standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level (95% in this case). 
Plugging in the values, we get:
CI = 645 ± 1.96*(31/√56) 
CI = (636.9, 653.1)
Therefore, the best choice is A.

A Random Sample of 56 Fluorescent Light Bulbs Has a Mean