According to the Bureau of Labor Statistics, the mean salary for registered nurses in Kentucky was $55,130. The distribution of salaries is assumed to be normally distributed with a standard deviation of $5,778. Someone would like to determine if registered nurses in Ohio have a greater average pay. To investigate this claim, a sample of 220 registered nurses is selected from the Ohio Board of Nursing, and each is asked their annual salary. The mean salary for this sample of 220 nurses is found to be $55,504.488. mean: μ y-bar = 55,130 standard deviation: σ y-bar = (round your answer to 4 decimal places) shape: the distribution of y-bar is normally distributed because the population of salaries is normally distributed. Using the distribution described, what is the probability of observing a sample mean of 55,504.488 or more? z = _______ (round to 2 decimal places) probability = __________ (include 4 decimal places)
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.
According to the Bureau of Labor Statistics, the
-
- mean: μ y-bar = 55,130
- standard deviation: σ y-bar = (round your answer to 4 decimal places)
- shape: the distribution of y-bar is normally distributed because the population of salaries is normally distributed.
Using the distribution described, what is the
-
- z = _______ (round to 2 decimal places)
- probability = __________ (include 4 decimal places)
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