The lengths of steel rods produced by a shearing process are normally distributed.A random sample of 10 rods is selected; the sample mean length is 119.05 centimetres; and the sample standard deviation is 0.10 centimetres.The 95% confidence interval for the population mean rod length is ___.
A)118.99 to 119.11
B)118.82 to 119.28
C)118.98 to 119.12
D)118.85 to 119.25
E)119.89 to 122.12

Question

Quizplus · Accepted Answer

We need to use the formula for a confidence interval for a population mean:

CI = X̄ ± Zα/2 * (σ/√n)

Where:
X̄ = sample mean 
Zα/2 = the critical value from the standard normal distribution for the desired level of confidence (0.95 in this case; so α = 0.025 and we can look up the critical value to be 1.96) 
σ = population standard deviation 
n = sample size

Substituting the given values, we get:

CI = 119.05 ± 1.96 * (0.10/√10) 
CI = 119.05 ± 0.039 
CI = (118.98, 119.12)

Therefore, the 95% confidence interval for the population mean rod length is 118.98 to 119.12 centimeters, which corresponds to choice C.

The Lengths of Steel Rods Produced by a Shearing Process