Question

The useful life of a bicycle bought at Basement-mart fits a log normal distribution with a mean of 16 months and a standard deviation of 11.33 months. Suppose that 68 bicycles are randomly chosen, and let

X_bar = the average useful life of a bicycle bought at Basement-mart, from a sample of 68 bicycles (in months)
X_bar ~ ___ (____, ____)

Answer 1

The average useful life of a bicycle bought at Basement-mart from a sample of 68 bicycles follows a normal distribution with a mean of 16 months and a standard deviation of 11.33 months divided by the square root of 68.

Step-by-step explanation:

To find the distribution of X_bar, the average useful life of a bicycle bought at Basement-mart from a sample of 68 bicycles, we need to use the properties of the log normal distribution. Since X_bar is an average, it follows a normal distribution with the same mean as the original distribution (16 months) and a standard deviation equal to the standard deviation of the original distribution divided by the square root of the sample size (√68). Therefore, X_bar ~ Normal(16, 11.33/√68).