The amount of time it takes a manager named Leila to complete an employee review is normally distributed with a mean of 46 minutes and a standard deviation of 8 minutes. Leila has 10 employees to review each month. Let X be the random variable representing the mean length of the 10 reviews. a. Fill in the blank, rounding your answers to 2 decimal places if needed. According to the Central Limit Theorem, X is approximately normal with a mean of  _______minutes and a standard error of the mean ______ minutes. b. Find the 75th percentile of X. Round your answer to two decimal places.  minutes c. Interpret your result: a. 75% of employee reviews will take longer than 47.71 minutes. b. 75% of samples of 10 employees will have an average time to complete reviews over 47.71 minutes.    c. 75% of employee reviews will take less than 47.71 minutes. d. 75% of samples of 10 employees will have an average time to complete reviews under 47.71 minutes.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...