a sample of 144 was taken from a population with a standard deviation of 36 inches. In this case the sample mean will be within how many inches of the population mean 99.7% of thew time?

9 inches

Step-by-step explanation:

The population is within 6 standard deviations of the mean with a confidence of 99.7 percent, 3 above and 3 below

The standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size

population standard deviation = 36

sample size = 144

standard deviation of the sample mean = 36 / sqrt (144)

=36/12

=3

The margin of error is the number of standard deviations above the mean * the standard deviations

margin of error = 3 * 3

= 9 inches