1. The national average SAT score (for verbal and math) is 1028. Assume a normal distribution with =σ 92. Round intermediate z-value calculations to two decimal places. What is the 97th percentile score? Round the answer to the nearest whole number.
2. Qualifying Test Scores To qualify for a medical study, an applicant must have a systolic blood pressure in the 80% of the middle range. If the systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 3, find the upper and lower limits of blood pressure a person must have to qualify for the study. Round final answers to 1 decimal place and intermediate z-value calculations to 2 decimal places. Applicants must have a lower blood pressure limit of ? and an upper blood pressure limit of ? to qualify for the study.
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 + ...
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