I. Find the area corresponding to the following z values and sketch the curve.  1. P ( 0 < z < 1.47 ) 2. P( -2.35 < z < 0 )  3. P( -2.59 < z < 0.41 ) 4. P ( -1.67 < z < 1.56 ) 5. P ( to the left of z = -1.96 ) II. Solve the problem carefully, sketch the curve.  1. The daily income of bank audition in SSS Commercial Bank is normally distributed with a mean of Php 675 and a standard deviation of Php 45. What is the z value for the income x of a bank auditor who earns Php 700 daily?  2. Johnny scored  72 in a quiz in Algebra for which the average score of the class was 65 with a standard deviation of 8. He also took a quiz in Statistics and scored 60 for which the average score of the class was 45, and the standard deviation was 12. Relative to other students in the class, did Johnny do better in Algebra or Statistics?

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 + ...