The mean number of pets per household is 2.96 with standard deviation 1.4. A sample of 52 households is drawn. Find the 74th percentile of the sample mean.
A) 3.74
B) 3.86
C) 2.57
D) 3.08

Question

Quizplus · Accepted Answer

The 74th percentile of the sample mean can be found using the formula for the mean of the sampling distribution (which is the same as the population mean) and the standard error of the mean. The standard error (SE) is calculated as the population standard deviation divided by the square root of the sample size: SE = 1.4 / sqrt(52). To find the 74th percentile, we use the Z-score corresponding to the 74th percentile in a standard normal distribution, which is approximately 0.67. The formula to find the specific value at the 74th percentile is: mean + Z * SE. Plugging in the values: 2.96 + 0.67 * (1.4 / sqrt(52)) = 3.08.

The Mean Number of Pets Per Household Is 2