Question

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?

Answer 1

Answer:

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