Suppose that the speed at which cars go on the freeway is normally distributed with mean 67 mph and standard deviation 10 miles per hour. Let X be the speed for a randomly selected car.
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.
As the population standard deviation is known, it can be said that the distribution follows a normal distribution. The mean and standard deviation of the sampling distribution of the sample mean is equal to μXˉ and respectively.
a.
In this case, the mean will be 67 and the standard deviation will be . Hence, the distribution can be written as,
| X∼N(67,10) |
b.
Calculate the corresponding z score as follows:
The probability that the traveling is more than 69 can be calculated as:
By using the standard normal table,
Hence, the probability that the traveling is more than 69 is,
| 0.4207 |
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