For a recent 10k run, the finishers are normally distributed with mean 63 minutes and standard deviation 10 minutes. Complete parts (a) through (d) below. Click here to view page 1 of the standard normal distribution table, Click here to view page 2 of the standard normal distribution table, a. Determine the percentage of finishers with times between 45 and 75 minutes. Approximately 84.9 % of finishers had times between 45 and 75 minutes. (Round to two decimal places as needed.) b. Determine the percentage of finishers with times less than 80 minutes. Approximately 95.54 % of finishers had times less than 80 minutes. (Round to two decimal places as needed.) c. Obtain and interpret the 35th percentile for the finishing times. The 35th percentile is minutes. (Round to two decimal places as needed.)
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 normal distribution is the most useful theoretical distribution for continuous variables.
For the normal distribution,
Mean = μ and
Standard deviation = σ, symbolically we write.
Given,
Population mean = μ = 63
Population standard deviation = σ = 10
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