Question

A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.2 gallons. A quality control manager took a simple random sample of 10 tanks from the production line. Let $\bar{X}$ denote their average capacity. If he were to increase the sample size to 40, which one of the following statements is TRUE about the standard deviation of $\bar{X}$? The standard deviation of $\bar{X}$ will reduce to its quarter. The standard deviation of $\bar{X}$ will reduce to its half. The standard deviation of $\bar{X}$ will double. The standard deviation of $\bar{X}$ will increase to its four times.

          A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that
the actual capacity of a randomly selected tank has a distribution that is
approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.2
gallons.
A quality control manager took a simple random sample of 10 tanks from the
production line. Let $\bar{X}$ denote their average capacity. If he were to increase the
sample size to 40, which one of the following statements is TRUE about the standard
deviation of $\bar{X}$?
The standard deviation of $\bar{X}$ will reduce to its quarter.
The standard deviation of $\bar{X}$ will reduce to its half.
The standard deviation of $\bar{X}$ will double.
The standard deviation of $\bar{X}$ will increase to its four times.

A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that
the actual capacity of a randomly selected tank has a distribution that is
approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.2
gallons.
A quality control manager took a simple random sample of 10 tanks from the
production line. Let X̅ denote their average capacity. If he were to increase the
sample size to 40, which one of the following statements is TRUE about the standard
deviation of X̅?
The standard deviation of X̅ will reduce to its quarter.
The standard deviation of X̅ will reduce to its half.
The standard deviation of X̅ will double.
The standard deviation of X̅ will increase to its four times.

Added by James C.

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