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Genrish500 [490]
4 years ago
9

As a sales person at scrapbooks and treasures Alyssa receives a monthly base pay plus commission on all that she sells she sells

$400 worth of merchandise in one month shoes paid $388 if she sells $1000 worth of merchandise in one month she is paid $520 find Alyssa salary when she sells $3300 worth of merchandise
Mathematics
1 answer:
max2010maxim [7]4 years ago
3 0
Let 
x =  base pay per month
y = commission per $1 of sales

Then the monthly pay for selling $100 of merchandise is
P = x + 100y

In one month, Alyssa earned $388 for selling $400 worth of merchandise.
Therefore
x + 400y = 388           (1)

In another month, she earned $520 for selling $1000 worth of merchandise.
Therefore
x + 1000y = 520        (2)

Subtract (1) from (2).
x + 1000y - (x + 400y) = 520 - 388
600y = 132
y = 0.22
From (1), obtain
x = 388 - 400y = 388 - 400*0.22 = 300

When Alyssa sells $3300 worth of merchandise, she earns
300 +0.22*3300 = $1026

Answer: $1026
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4 years ago
According to a 2009 Reader's Digest article, people throw away approximately 11% of what they buy at the grocery store. Assume t
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0.14% probability that the sample proportion exceeds 0.2

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 108, p = 0.11

So

\mu = E(X) = np = 108*0.11 = 11.88

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{108*0.11*0.89} = 3.2516

What is the probability that the sample proportion exceeds 0.2

This is 1 subtracted by the pvalue of Z when X = 0.2*108 = 21.6. So

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

Z = \frac{21.6 - 11.8}{3.2516}

Z = 2.99

Z = 2.99 has a pvalue of 0.9986

1 - 0.9986 = 0.0014

0.14% probability that the sample proportion exceeds 0.2

8 0
4 years ago
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