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ankoles [38]
3 years ago
11

sume that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally dis

tributed with a mean of $0.35 and a standard deviation of $0.33. Based on this information, what is the probability that a randomly selected stock will close up $0.75 or mor
Mathematics
1 answer:
Darina [25.2K]3 years ago
4 0

Answer:

0.1131 = 11.31% probability that a randomly selected stock will close up $0.75 or more.

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.

Normally distributed with a mean of $0.35 and a standard deviation of $0.33.

This means that \mu = 0.35, \sigma = 0.33.

What is the probability that a randomly selected stock will close up $0.75 or more?

This is 1 subtracted by the p-value of Z when X = 0.75. So

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

Z = \frac{0.75 - 0.35}{0.33}

Z = 1.21

Z = 1.21 has a p-value of 0.8869.

1 - 0.8869 = 0.1131

0.1131 = 11.31% probability that a randomly selected stock will close up $0.75 or more.

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8 0
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Ibuki factored 12x^7as (4x^3)(3x^4)
Marina86 [1]

Answer:

Both are correct.

Step-by-step explanation:

The key understanding here is that you can factor a monomial in many different ways!

To check if any of the factorizations is correct, we can multiply the factors and see if their product is really 12x^712x

7

12, x, start superscript, 7, end superscript.

Hint #22 / 4

\begin{aligned} (\blueD{4}\maroonD{x^3})(\blueD{3}\maroonD{x^4})&=(\blueD{4})(\blueD{3})(\maroonD{x^3})(\maroonD{x^4}) \\\\ &=\blueD{12}\maroonD{x^7} \end{aligned}

(4x

3

)(3x

4

)

​

 

=(4)(3)(x

3

)(x

4

)

=12x

7

​

So Ibuki is correct!

Hint #33 / 4

\begin{aligned} (\blueD{2}\maroonD{x^6})(\blueD{6}\maroonD{x})&=(\blueD{2})(\blueD{6})(\maroonD{x^6})(\maroonD{x}) \\\\ &=\blueD{12}\maroonD{x^7} \end{aligned}

(2x

6

)(6x)

​

 

=(2)(6)(x

6

)(x)

=12x

7

​

So Melodie is also correct!

Both Ibuki and Melodie are correct.

8 0
3 years ago
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