The speeds of cars travelling on a certain highway are normally distributed with mean 98 km/h and standard deviation 9 km/h. a) Find the proportion of cars travelling more than 95 km/h. b) If the police follow a policy of ticketing only the fastest 4 percent, at what speed do the police start to issue tickets?
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.
1. The speeds of cars travelling on a certain highway are
a) Find the proportion of cars travelling more than 95 km/h.
b) If the police follow a policy of ticketing only the fastest 4 percent, at what speed do the police start to issue tickets?
2. The number of cups of coffee, X, a Statistics professor drinks on a day is either 0, 1, 2, 3, 4 or 5. The probability distribution of X is given by
x 0 1 2 3 4 5
p(x) 0.2 0.25 0.25 0.2 0.05 0.05
a) Calculate the expected value of X.
b) Calculate the standard deviation of X.
c) Suppose that two dollars are charged for the first cup of coffee and 40 cents for each additional cup of coffee. How much is expected for the Statistics professor to pay for the coffee on a typical day?
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