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3 years ago

Simplify {n - 1 - [n - 1 - (n - 1)]}.

Mathematics

2 answers:

adelina 88 [10]3 years ago

8 0

{n - 1 - [n - 1 - (n - 1)]}

=n - 1 - n + 1 + n - 1

=n -1

artcher [175]3 years ago

4 0

Don't forget the invisble negative ones to distriute
do inside to outside

{n-1-1[n-1-1(n-1)]}
do inside
{n-1-1[n-1-n+1]}
simplify inner parenthasees
{n-1-1[n-n+1-1]}
{n-1-1[0]}
multply
{n-1-0}
add
n-1-0=n-1

it is n-1 simplified

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3 years ago

Suppose that in one region of the country the mean amount of credit card debt perhousehold in households having credit card debt

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Answer:

The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 15250, \sigma = 7125, n = 1600, s = \frac{7125}{\sqrt{1600}} = 178.125$

The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly

This probability is the pvalue of Z when X = 1600 + 300 = 1900 subtracted by the pvalue of Z when X = 1600 - 300 = 1300. So

X = 1900

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{1900 - 1600}{178.125}$

$Z = 1.68$

$Z = 1.68$ has a pvalue of 0.9535.

X = 1300

$Z = \frac{X - \mu}{s}$

$Z = \frac{1300 - 1600}{178.125}$

$Z = -1.68$

$Z = -1.68$ has a pvalue of 0.0465.

0.9535 - 0.0465 = 0.907.

The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.

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3 years ago

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Answer:

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Step-by-step explanation:

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We will use permutation formula to solve our given problem as:

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