The ages of people in a large group chat are approximately normally distributed with amean of 20.73 and a standard deviation of 2.66. (a) Determine the standard score (rounded to two decimal places) and percentile (rounded to the nearest whole number) of a 19-year-old. (b) Approximately what percentage of people in the chat are over 19.5 years old? (Round to the nearest whole number.) (c) What age would someone have to be in order to be at the 60th percentile? (Round to one decimal place.)
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 ages of people in a large group chat are approximately
(a) Determine the standard score (rounded to two decimal places) and percentile (rounded to the nearest whole number) of a 19-year-old.
(b) Approximately what percentage of people in the chat are over 19.5 years old? (Round to the nearest whole number.)
(c) What age would someone have to be in order to be at the 60th percentile? (Round to one decimal place.)
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how is 0.46= .32276 because on the z table it's 32.64 so where does the .32276 come from
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