If a normal has a mean of 38.0 and a standard deviation of 1.25, what is the value of the random variable X that has an area to its right equal to 0.3121
If a normal has a mean of 33.7 and a standard deviation of 10.5, what is the value of the random variable X that has an area to its left equal to 0.9904?
During the fall season of racing at Dover International Speedway, the mean speed of the cars racing there was found to be 158.9 mph with a standard deviation of 6.7 mph. What speed represents the 30th percentile for speeds of race cars at Dover Speedway? Assume that the racing speeds are normally distributed.
Suppose that preschoolers spend a mean of 25 hours per week in daycare with a standard deviation of 5 hours per week. A newspaper journalist wants to point out that preschoolers are staying in daycares too long, from his perspective. If he only looks at the extreme of the distribution, that is the top 3%, what's the minimum number of hours per week those preschoolers spend in daycare? Assume that the number of hours per week that preschoolers spend in daycare are normally distributed.
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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