A company wants to estimate the time its trucks take to drive from city A to cityB. The standard deviation is known to be 12 minutes. What sample size is required in order that the error will not exceed ±2 minutes, with 95 percent confidence?
A)12 observations
B)139 observations
C)36 observations
D)129 observations

Question

Quizplus · Accepted Answer

To estimate the sample size required for a given margin of error with a known standard deviation and confidence level, the formula is $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the desired confidence level (1.96 for 95%), $\sigma$ is the standard deviation (12 minutes), and $E$ is the margin of error (2 minutes). Plugging in the values: $n = \left(\frac{1.96 \cdot 12}{2}\right)^2 = 138.24$, which rounds up to 139 observations.

A Company Wants to Estimate the Time Its Trucks Take