For a statistics project, Zenon decided to investigate if students at his school prefer name-brand potato chips to store-brand potato chips. He prepared two identical bowls of chips, filling one with name-brand chips and the other with store-brand chips. Then, he selected a random sample of 30 students, had each student try both types of chips in random order, and recorded which type of chip each student preferred. Assume that 50% of students at Zenon’s school prefer the name-brand chips. Let X = the number of students in the sample that prefer the name-brand chips.   a, Calculate the mean and standard deviation.   b. Interpret the standard deviation      (c)  Justify the distribution of X is approximately normal.     (d) Calculate the probability that 19 or more of the students will prefer the name-brand chips.

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 + ...