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Tatiana [17]
3 years ago
13

Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of mu equals 24.4 in.

and a standard deviation of sigma equals 1.2 in. These data are often used in the design of different​ seats, including aircraft​ seats, train​ seats, theater​ seats, and classroom seats. Instead of using 0.05 for identifying significant​ values, use the criteria that a value x is significantly high if​ P(x or ​greater)less than or equals0.01 and a value is significantly low if​ P(x or ​less)less than or equals0.01. Find the​ back-to-knee lengths separating significant values from those that are not significant. Using these​ criteria, is a​ back-to-knee length of 26.6 in. significantly​ high?
Mathematics
1 answer:
solong [7]3 years ago
6 0

Answer:

P(X \geq 26.6) = 0.0336, which is greater than 0.01. So a back-to-knee length of 26.6 in. is not significantly high.

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

\mu = 24.4, \sigma = 1.2

In this problem, a value x is significantly high if:

P(X \geq x) = 0.01

Using these​ criteria, is a​ back-to-knee length of 26.6 in. significantly​ high?

We have to find the probability of the length being 26.6 in or more, which is 1 subtracted by the pvalue of Z when X = 26.6. So

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

Z = \frac{26.6 - 24.4}{1.2}

Z = 1.83

Z = 1.83 has a pvalue of 0.9664.

1 - 0.9664 = 0.0336

P(X \geq 26.6) = 0.0336, which is greater than 0.01. So a back-to-knee length of 26.6 in. is not significantly high.

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Ksenya-84 [330]

Answer:

  x = -7/9

Step-by-step explanation:

The usual recommendation is to clear fractions first. Here, you can do that by multiplying both sides of the equation by 6.

  6(-1/2(3x -4) +3x) = 6(5/6)

  -9x +12 +18x = 5 . . . . . . . . . simplify

  9x = -7 . . . . . . . . . . . . . . . . . subtract 12

  x = -7/9 . . . . . .divide by 9

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Another way to do this is to eliminate parentheses first.

  -3/2x +2 +3x = 5/6

  3/2x = -7/6 . . . . . . . . . collect terms, subtract 2

  x = (-7/6)(2/3) = -7/9 . . . . multiply by 2/3

3 0
2 years ago
Can you please help me​
IRISSAK [1]

Answer:

Step-by-step explanation:

1. HI // KL , J is midpoint of  HL     1. Given

2. ∠IHJ ≅ ∠JLK                             2. Alternate interior angles are congruent

3. ∠IJH ≅ ∠KJL                              3. Vertically opposite angles

4. HJ ≅   JL                                     4. Given

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3 0
2 years ago
Evaluate (-A) 2 for A = 5, B = -4, and C= 2.<br> 0-25<br> -10<br> 10<br> 25
Alenkinab [10]

Answer:

-10

Step-by-step explanation:

Substitute 5 into the equation

(-5)2

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4 0
3 years ago
20 points!<br> I need help (asap!!)
EastWind [94]

Answer:

<h2>x = 5</h2><h2>OB = 36</h2><h2>BE = 54</h2>

Step-by-step explanation:

We know that the medians of the triangle divides in a ratio of 2:1. Therefore we have the equation:

\dfrac{9x-9}{2x+8}=\dfrac{2}{1}                <em>cross multiply</em>

1(9x-9)=2(2x+8)             <em>use distributive property a(b + c) = ab + ac</em>

9x-9=(2)(2x)+(2)(8)

9x-9=4x+16                 <em>add 9 to both sides</em>

9x=4x+25                <em>subtract 4x from both sides</em>

5x=25             <em>divide both sides by 5</em>

\boxed{x=5}

OB=9x-9\to OB=9(5)-9=45-9=\boxed{36}

OE=OB:2\to OE=36:2=18\to BE=BO+OE\to BE=36+18=54


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3 years ago
What is 30% of 25.45?
Alekssandra [29.7K]

Answer:

7.635

Step-by-step explanation:

i hope it helps:)

3 0
3 years ago
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