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Zielflug [23.3K]
3 years ago
7

The wall in the family room is exactly 15 feet long. Your couch is 9feet and 3 inches long. Once the couch is placed how much ro

om is left for your end table?
Mathematics
1 answer:
sdas [7]3 years ago
6 0

Answer:

5 feet 9 in.

Step-by-step explanation:

15 feet = 180 in.

9 feet = 108 in.

108 in. + 3 in. = 111

180 in. - 111 in. = 69 in.

69 in. = 5 feet 9 in.

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The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.7 millimeters and a standard deviati
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Answer:

The diameter that separates the top 3% is of 5.85 millimeters, and the one which separates the bottom 3% is of 5.55 millimeters.

Step-by-step explanation:

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.

Mean of 5.7 millimeters and a standard deviation of 0.08 millimeters.

This means that \mu = 5.7, \sigma = 0.08

Top 3%

The 100 - 3 = 97th percentile, which is X when Z has a p-value of 0.97, so X when Z = 1.88.

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

1.88 = \frac{X - 5.7}{0.08}

X - 5.7 = 1.88*0.08

X = 5.85

Bottom 3%

The 3rd percentile, which is X when Z has a p-value of 0.03, so X when Z = -1.88.

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

-1.88 = \frac{X - 5.7}{0.08}

X - 5.7 = -1.88*0.08

X = 5.55

The diameter that separates the top 3% is of 5.85 millimeters, and the one which separates the bottom 3% is of 5.55 millimeters.

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Step-by-step explanation:

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