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tiny-mole [99]
3 years ago
5

. The time required for a technician to machine a specific component is normally distributed with a mean of 2 hours and a standa

rd deviation of 17 minutes. (a.) What is the probability that the technician can machine one component in 1.5 hours or less? (b.) What is the probability that the technician will require at least 2.75 hours to complete one component? (be sure to work in hours)
Mathematics
1 answer:
erma4kov [3.2K]3 years ago
4 0

Answer:

a) There is a 3.84% probability that the technician can machine one component in 1.5 hours or less.

b) There is a 0.42% probability that the technician will require at least 2.75 hours to complete one component

Step-by-step explanation:

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}

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.

In this problem, we have to be careful. The mean is in hours, while the standard deviation is in minutes. I am going to work with both in hours, as the problem states. 17 minutes is 0.283 hours, so:

\mu = 2, \sigma = 0.283

(a.) What is the probability that the technician can machine one component in 1.5 hours or less?

This probability is the pvalue of the Zscore when X = 1.5. So:

Z = \frac{1.5 - 2}{0.283}

Z = \frac{-0.5}{0.283}

Z = -1.77

Z = -1.77 has a pvalue of 0.0384.

This means that there is a 3.84% probability that the technician can machine one component in 1.5 hours or less.

(b.) What is the probability that the technician will require at least 2.75 hours to complete one component?

The pvalue of the score of X = 2.75 is the probability that the technican will require less than 2.75 hours to complete one component. The probability that he will require at least 2.75 hours to complete one component is 1 subtracted by this pvalue. So:

Z = \frac{2.75 - 2}{0.283}

Z = \frac{0.75}{0.283}

Z = 2.65

Z = 2.65 has a pvalue of 0.99598.

This means that the probability that the technican will require at least 2.75 hours to complete one component is 1 - 0.99598 = 0.0042 = 0.42%.

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Answer:

(-1,1), (1,3), (2,2)

Step-by-step explanation:

To dilate an object, we need to multiply the x and y values by the given scale factor.

In this case the scale factor is 1/3 --> 1/3(x, y)

Before-> After dilation

1/3(-3,3) = (-1,1)

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Please leave a 'thanks' if this helps!

8 0
3 years ago
If it takes 4 men 6hours to repair a road, how long will it take 7 men to do the job if they work at the same rate.
Crank
Tricky question. This isn't a ratio question even though it seems like one.

First divide 7 by 4.
7 \div 4 = 1.75

With more men, the hours taken to repair a road will be even shorter.

So next divide 6 by 1.75.
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Answer : It'll take 3.43 hours to do the job if they work at the same rate.

Hope this helps. - M
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3 years ago
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s344n2d4d5 [400]

Answer:

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Step-by-step explanation:

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A) The peak of the curve has coordinates (3, 45). Thus the maximum is 45 hundred dollars. It occurs when 3 hundred dollars are spent on advertisiing.
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Step-by-step explanation:

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