(ii) Sample of size 50 (i) Sample of size 30 12 7 8 - 6 6 4 T3 2 2 mott 1 11 10 12 0 9 7 0 12 11 10 9 (iii) Sample of size 100 20 15 10 5+ 12 11 10 9 8O 10 Frequency LO Frequency 4 25 Frequency
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.
Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on the next page are based on random samples of size 30,50 and 100 from the same population.
a. Using the midpoint labels of the three histograms, what would you say about the estimated
b. The population distribution from which the samples were drawn is symmetric and mound shaped, with the top of the mound at 10,95% of the data between 8 and 12, and 99.7% of data between 7 and 13. How well does each histogram reflect these characteristics?
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