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Alexxx [7]
3 years ago
12

3 books cost $150 and one book is half of the total amount of the other two books. what is the amount of the books

Mathematics
1 answer:
Margaret [11]3 years ago
6 0
$50 each
(2 books + 1 book : $100 + $50 = $150)
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Suppose a continuous probability distribution has an average of μ=35 and a standard deviation of σ=16. Draw 100 times at random
yulyashka [42]

Answer:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

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 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

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

For sums, we have that the mean is \mu*n and the standard deviation is s = \sigma \sqrt{n}

In this problem, we have that:

\mu = 100*35 = 3500, \sigma = \sqrt{100}*16 = 160

This probability is the pvalue of Z when X = 4000 subtracted by the pvalue of Z when X = 3000.

X = 4000

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

By the Central Limit Theorem

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

Z = \frac{4000 - 3500}{160}

Z = 3.13

Z = 3.13 has a pvalue of 0.9991

X = 3000

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

Z = \frac{3000 - 3500}{160}

Z = -3.13

Z = -3.13 has a pvalue of 0.0009

0.9991 - 0.0009 = 0.9982

So the correct answer is:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

5 0
3 years ago
If the measures of the angles of a quadrilateral are in the ratio of 3 : 4 : 5 : 8, find the measure (in degrees) of each angle.
BabaBlast [244]

Answer:

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Step-by-step explanation:

6 0
2 years ago
(0.00032)(5.2x10^6)/6.4x10^5
Elena-2011 [213]

Answer:

26000000

Step-by-step explanation:

sorry if its wrong

7 0
2 years ago
Use mathematical induction to prove that the statement is true for every positive integer n.
Natali [406]

Answer:

3x-4v

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3 0
2 years ago
Solve:<br> 3x−5 = 9. <br> A. x = −3 <br> B.x = 2 <br> C.x = 7 <br> D.x = 8
Alina [70]

Answer:

Step-by-step explanation:

3x-5=9

3x-5+5=9+5

3x=14

\frac{3x}{3}=\frac{14}{3}

x=\frac{14}{3}

x ≈ 4.66667

4 0
3 years ago
Read 2 more answers
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