The loan amounts of loans originated by a large insurance company lender have a mean of $6.74 million with a standard deviation of $15.37 million. The variable “loan amount” is known to have a right-skewed distribution.a) Using units of millions of dollars, determine the sampling distribution of the sample mean for samples of size 200. Interpret your result.b) Repeat part (a) for samples of size 600.c) Why can you still answer parts (a) and (b) when the distribution of loan amounts is not normal, but rather right-skewed?d) What is the probability that the sampling error made in estimating the population mean loan amount by the mean loan amount of a simple random sample of 200 loans will be at most $1 million?e) Repeat part (d) for samples of size 600.

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

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ISBN:9780079039897

Author:Carter

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Chapter10: Statistics

Section10.4: Distributions Of Data

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The loan amounts of loans originated by a large insurance company lender have a mean of $6.74 million with a standard deviation of $15.37 million. The variable “loan amount” is known to have a right-skewed distribution.

a) Using units of millions of dollars, determine the sampling distribution of the sample mean for samples of size 200. Interpret your result.
b) Repeat part (a) for samples of size 600.
c) Why can you still answer parts (a) and (b) when the distribution of loan amounts is not normal, but rather right-skewed?
d) What is the probability that the sampling error made in estimating the population mean loan amount by the mean loan amount of a simple random sample of 200 loans will be at most $1 million?
e) Repeat part (d) for samples of size 600.

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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