The results of a certain medical test are normally distributed with a mean of 124 and a standard deviation of 20. Convert the given results into z-scores, and then use the table below to find the percentage of people with readings between 158 and 178. 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Z-score Percentile 97.72 96.41 2.9 99.81 93.32 94.52 95.54 97.13 86.43 2.2 98.61 90.32 2.4 99.18 84.13 88.49 91.92 3.0 2.7 99.65 2.8 3.5 2.3 98.93 2.1 2.5 2.6 Z-score Percentile 98.21 99.38 99.53 99.74 99.87 99.98 The percentage of people with readings between 158 and 178 is %. (Round the final answer to the nearest hundredth as needed. Round the z-score to the nearest tenth 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.
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