Question

A random sample of electronic components had the following operational times before failure, in hours: 322, 350, 346, 347, 335, 323, 341, 355, 329. Assume the population standard deviation is 36 and that the population is approximately normal. Construct a 90% confidence interval for the population mean operational time before failure.

a) (325.2, 349.6)
b) (328.4, 348.1)
c) (331.7, 346.8)
d) (326.9, 347.6)

Answer 1

To construct a 90% confidence interval for the population mean operational time before failure, calculate sample mean, find z-score, calculate margin of error, and define the confidence interval range using the formula.

Step-by-step explanation:

To construct a 90% confidence interval for the population mean operational time before failure, we can use the formula:

CI = sample mean ± (z-score) * (population standard deviation / sqrt(sample size))

Step 1: Calculate the sample mean of the operational times, which is 339.7.

Step 2: Find the z-score for a 90% confidence level, which is approximately 1.645.

Step 3: Calculate the margin of error by multiplying the z-score by the standard deviation divided by the square root of the sample size. This is approximately 5.86.

Step 4: The confidence interval is then (339.7 - 5.86, 339.7 + 5.86), which simplifies to (333.84, 345.56).

Therefore, the correct answer is d) (326.9, 347.6).