Q1)According to a PEW Research Center survey, the mean student loan at graduation is $25,000. Suppose that student loans are normally distributed with a standard deviation of $5,000. A graduate with a student loan is selected at random. Find the following probabilities.The loan is greater than $30,000.The loan is less than $22,500.The loan falls between $20,000 and $32,000. Q2) Probability of a Negative Return on InvestmentConsider an investment whose return is normally distributed with a mean of 10% and a standard deviation of 5%.Determine the probability of losing money.Find the probability of losing money when the standard deviation is equal to 10%.[Hint: P(X < 0) ]

Q1) Given:μ = population mean = $25,000σ = population standard deviation = $5000 1.in order to get…

Answered: Q1)According to a PEW Research Center…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.7: Probability

Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...

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Q1)According to a PEW Research Center survey, the mean student loan at graduation is $25,000. Suppose that student loans are normally distributed with a standard deviation of $5,000. A graduate with a student loan is selected at random. Find the following probabilities.

The loan is greater than $30,000.
The loan is less than $22,500.
The loan falls between $20,000 and $32,000.

Q2) Probability of a Negative Return on Investment

Consider an investment whose return is normally distributed with a mean of 10% and a standard deviation of 5%.

Determine the probability of losing money.
Find the probability of losing money when the standard deviation is equal to 10%.

[Hint: P(X < 0) ]

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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