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2 years ago

13

Michael has $1.95 totally in his collection, consisting of quarters and nickels. The number of nickels is three more than the nu

mber of quarters. How many nickels and how many quarters does Michael have?

2 answers:

madreJ [45]2 years ago

4 0

6 quarters = $1.50
9 Nickels = $0.45

Total= $1.95

Answer is 6 quarters and 9 nickels.<span />

Setler79 [48]2 years ago

3 0

He has 7 quarters and 9 nickels because $1.50+ $.45= $1.95.

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

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$X \sim N(\mu=100,\sigma=6)$

And let $\bar X$ represent the sample mean, by the central limit theorem, the distribution for the sample mean is given by:

$\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})$

a. What are the mean and variance of the sampling distribution for the sample means?

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$\mu_{\bar X}=100$ $\sigma^2_{\bar X}=1.2^2=1.44$

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$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

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$z=\frac{101-100}{\frac{6}{\sqrt{25}}}=0.833$

And we want to find this probability:

$P(\bar X >101)=1-P(\bar X$

On this last step we use the complement rule.

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