The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.3 miles per gallon. (a) What proportion of hybrids gets over 61 miles per gallon? (b) What proportion of hybrids gets 52 miles per gallon or less? (c) What proportion of hybrids gets between 59 and 62 miles per gallon? (d) What is the probability that a randomly selected hybrid gets less than 45 miles per gallon? As demonstrated in lecture, for each question draw an appropriate distribution function (graph) to represent the data, shade the desired area and show all work, including what you input into your calculator to attain your results.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The mean gas mileage for a hybrid car is
miles per gallon. Suppose that the gasoline mileage is approximately
miles per gallon. (a) What proportion of hybrids gets over
miles per gallon? (b) What proportion of hybrids gets
miles per gallon or less?
proportion of hybrids gets between
and
miles per gallon? (d) What is the probability that a randomly selected hybrid gets less than
miles per gallon? As demonstrated in lecture, for each question draw an appropriate distribution
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