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Suppose that the sitting back-to-knee length for a group of adults has a normal distribution with a mean of μ=22.5 in. and a standard deviation of σ=1.1 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) ≤0.01 and a value is significantly low if P(x or less) ≤0.01.Find the back-to-knee lengths separating significant values from those that are not significant.

Answers

Answer 1

Answer:

Answer:

Measures equal or lower than 19.94 inches are significantly low.

Measures equal or higher than 25.06 inches are significantly high.

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:

$Z = (X - \mu)/(\sigma)$

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:

$\mu = 22.5, \sigma = 1.1$

Find the back-to-knee lengths separating significant values from those that are not significant.

Significantly low

In this exercise, a value is going to be to significantly low if it has a pvalue of 0.01 or less. So we have to find X when Z has a pvalue of 0.01. This is between $Z = -2.32$ and $Z = -2.33$ , so we use $Z = -2.325$

$Z = (X - \mu)/(\sigma)$

$-2.325 = (X - 22.5)/(1.1)$

$X - 22.5 = -2.325*1.1$

$X = 19.94$

Measures equal or lower than 19.94 inches are significantly low.

Significantly high

In this exercise, a value is going to be to significantly high if it has a pvalue of 0.99 or more. So we have to find X when Z has a pvalue of 0.99. This is $Z = 2.325$ . So:

$Z = (X - \mu)/(\sigma)$

$2.325 = (X - 22.5)/(1.1)$

$X - 22.5 = 2.325*1.1$

$X = 25.06$

Measures equal or higher than 25.06 inches are significantly high.

Answer 2

Answer:

Final answer:

To find the separating back-to-knee lengths, we calculate the corresponding z-scores for the given probabilities. Using the standard normal distribution table, we find that the separating values are 24.78 inches for significantly high lengths and 20.22 inches for significantly low lengths.

Explanation:

To find the back-to-knee lengths separating significant values from those that are not significant, we need to calculate the z-scores corresponding to the given probabilities. For a value to be significantly high, we look for a z-score such that the area to its right is 0.01. Using the standard normal distribution table, we find that z = 2.33. Similarly, for a value to be significantly low, we look for a z-score such that the area to its left is 0.01. Again using the table, we find that z = -2.33. Converting these z-scores back to actual back-to-knee lengths, we can calculate the separating values as: 22.5 + (2.33 * 1.1) = 24.78 inches for significantly high lengths, and 22.5 - (2.33 * 1.1) = 20.22 inches for significantly low lengths.

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A floor plan is drawn using a scale of (3 cm)/(15ft) What length is represented by 1 centimeter ?

Answers

Answer:

5 feet per 1 cm

Step-by-step explanation:

Answer:

The answer is 5 feet.

Step-by-step explanation:

Set up a proportion.

3/15 = 1/x (x being the number of feet)

Cross multiply.

3x = 15

Solve for x. (divide both sides by 3)

x = 5

I hope this helps! :)

The local newspaper has letters to the editor from 70 people. If this number represents 4% of all of the newspapers readers, how many readers does the newspaper

Answers

Final answer:

The local newspaper has 1,750 readers.

Explanation:

To find the total number of newspaper readers, we can set up a proportion using the given information. Let x be the total number of newspaper readers. We can write the proportion:

70/ x = 4/100

Cross multiplying, we have:

70 * 100 = 4 * x

7000 = 4 * x

Dividing both sides by 4, we find:

x = 7000 / 4

x = 1750

Therefore, the newspaper has 1,750 readers.

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Answer:

1750

Step-by-step explanation:

We first find the rate

70/4

= 17.5

We know 17.5 is 1% of the people that read newspaper, we will multiply 17.5 by 100 as it would represent 100% of the people

17.5 * 100

= 1750

Pasta costs £1.50 per kg.
How much does 600g of pasta cost?

Answers

The solution is, 600g of pasta cost £ 0.9.

What is division?

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

Pasta costs £1.50 per kg.

now we have to find,

How much does 600g of pasta cost

we know,

1 kg = 1000 grm.

so, we get,

1000 g Pasta costs £1.50

so, 1 g Pasta costs £1.50/1000

so, 600 g Pasta costs £1.50/1000 * 600

= £ 0.9

Hence, The solution is, 600g of pasta cost £ 0.9.

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Differentiate Functions of Other Bases In Exercise, find the derivative of the function.y = 3x

Answers

Answer:

The derivative of the function is 3.

Step-by-step explanation:

The derivative of $a*x^(n)$ is $a*n*x^(n-1)$ . The derivative of 20x is 20, for example. The derivative of $40x^(4)$ is $160x^(3)$ .

In this problem

It aks the derivative of a function, which is 3x. Applying the rule that is explained above, we have that the derivative of 3x is 3.

So the derivative of the function is 3.

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