Question

The manager of a gasoline supply corporation wants to estimate the actual amount of gasoline contained in standard 42-gallon barrels purchased from a nationally known manufacturer. The manufacturer’s specifications state that the amount of gasoline is normally distributed with a standard deviation of 0.65 gallon. A random sample of 25 barrels is selected, and the sample mean amount of gasoline per 42-gallon barrel is 42.15 gallons. Construct a 90% confidence interval estimate for the population mean amount of gasoline contained in a standard 42-gallon barrel.

Answer 1

Suppose, random variable X denotes amount of gasoline (in gallons) in a 42-gallon barrel.

Population standard deviation is known. So, we have to use one sample z-test statistic.

Corresponding statistic is given by

Here,

Sample size

Sample mean

Population standard deviation

We know,

  [Using R-code 'qnorm(1-(1-0.90)/2)']

Hence, 90% confidence interval is given by (41.93617, 42.36383).