John has integers 1:10. He randomly draws 5 without replacement and reasons that he could estimate the 80th percentile of his 10 integers, the value 8, by taking the 2nd largest sampled value; that is the 4th value in order from smallest to largest. (a) Applying this approach repetitively, what proportion of the time will he accurately estimate the value 8? (b) Underestimate? (c) Overestimate? Here is how I am thinking to solve the problem: The only possible numbers in position 4 would be 4, 5, 6, 7, 8, 9. So, the proportion of time it'd be an 8 would be 1/6. an underestimate would be the numbers 4, 5, 6, and 7 for a proportion of time to be 4/6 or 2/3. an overestimate would be the number 9 for a proportion of 1/6. Is this correct?
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.
John has integers 1:10. He randomly draws 5 without replacement and reasons that he could estimate the 80th percentile of his 10 integers, the value 8, by taking the 2nd largest sampled value; that is the 4th value in order from smallest to largest.
(a) Applying this approach repetitively, what proportion of the time will he accurately estimate the value 8?
(b) Underestimate?
(c) Overestimate?
Here is how I am thinking to solve the problem: The only possible numbers in position 4 would be 4, 5, 6, 7, 8, 9. So, the proportion of time it'd be an 8 would be 1/6.
an underestimate would be the numbers 4, 5, 6, and 7 for a proportion of time to be 4/6 or 2/3.
an overestimate would be the number 9 for a proportion of 1/6.
Is this correct?
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