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Leni [432]
3 years ago
8

A bill from a plumber was $306 The plumber charged $150 for parts and $52 per hour for labor. How long did ths plumber work at h

is job?
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
6 0
We can make an equation from this.
Our intial value is 150 for parts, and he works for 52 dollars an hour.
We can define <em /><em>h</em> for hours and <em /><em>c</em> for total cost.
Therefore, we have:
c = 150 + 52h.
We can set this equal to 306 dollars, as that's the given total cost:
306 = 150 + 52h
Subtract 150 from both sides:
52h = 156
Divide both sides by 2:
h = 3
He worked 3 hours.
hope this helped!

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A sample size 25 is picked up at random from a population which is normally
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b) P(98 < X < 100) = 0.4525

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

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For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 100 and variance of 36.

This means that \mu = 100, \sigma = \sqrt{36} = 6

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This means that n = 25, s = \frac{6}{\sqrt{25}} = 1.2

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Z = -1.67

Z = -1.67 has a pvalue of 0.0475

0.5 - 0.0475 = 0.4525

So

P(98 < X < 100) = 0.4525

6 0
3 years ago
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