Answered: The mean starting salary for nurses is…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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The mean starting salary for nurses is $67,694 nationally ("Staff nurse -," 2013).
The standard deviation is approximately $10,333. The starting salary is not
normally distributed but it is mound shaped. A sample of 42 starting salaries for
nurses is taken.
a.) State the random variable.
b.) What is the mean of the sample mean?
c.) What is the standard deviation of the sample mean?
d.) What is the sampling distribution of the sample mean? Why?
e.) Find the probability that the sample mean is more than $75,000.
f.) Find the probability that the sample mean is less than $60,000.
g.) If you did find a sample mean of more than $75,000 would you find that
unusual? What could you conclude?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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