Does this graph represent a function?

The cost of a salad bar is $4 per pound graph it

Virty [35]

X y
1 = 4
2 = 8
3 = 12
4 = 16
X = pounds
y = price

3 0

3 years ago

The Dow Jones Industrial Average has had a mean gain of 432 pear year with a standard deviation of 722. A random sample of 40 ye

trasher [3.6K]

Answer:

66.98% probability that the mean gain for the sample was between 250 and 500.

Step-by-step explanation:

To solve this problem, it is important to know the Normal probability distribution and the Central limit theorem.

Normal probability distribution

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:

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

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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

In this problem, we have that:

$\mu = 432, \sigma = 722, n = 40, s = \frac{722}{\sqrt{40}} = 114.16$

What is the probability that the mean gain for the sample was between 250 and 500?

This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 250.

So

X = 500

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

By the Central Limit Theorem

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

$Z = \frac{500 - 432}{114.16}$

$Z = 0.6$

$Z = 0.6$ has a pvalue of 0.7257.

X = 250

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

By the Central Limit Theorem

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

$Z = \frac{250 - 432}{114.16}$

$Z = -1.59$

$Z = -1.59$ has a pvalue of 0.0559.

So there is a 0.7257 - 0.0559 = 0.6698 = 66.98% probability that the mean gain for the sample was between 250 and 500.

8 0

3 years ago

Harry is one third as old as his father. If his father is x 12 years old, how old is Harry? StartFraction x over 3 EndFraction 4

Mama L [17]

The age of the Harry in the terms of variable <em>x, </em>as the age of his father is (x+4) is represent with following equation.

$\sqrt{3}x+4$

<h3>How to write algebraic expression? </h3>

Algebraic expression are the expression which consist the variables, coefficients of variables and constants.

The algebraic expression are used represent the general problem in the mathematical way to solve them.

Harry is one third as old as his father and his father is x+12 years old.To find the age of Harry, we need to convert the given statement into the algebraic expression.

Suppose the age of the Harry is <em>a</em> years and the age of his father is<em> b</em> years. Now Harry is one third as old as his father, thus

$a=\dfrac{1}{3}b$