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Life Expectancies In a study of the life expectancy of people in a certain geographic region, the mean age at death was years an

Sphinxa [80]

Answer:

The probability that the mean life expectancy of the sample is less than X years is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean life expectancy, $\sigma$ is the standard deviation and n is the size of the sample.

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 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.

Central Limit Theorem

The Central Limit Theorem establishes 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.

We have:

Mean $\mu$ , standard deviation $\sigma$ .

Sample of size n:

This means that the z-score is now, by the Central Limit Theorem:

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

Find the probability that the mean life expectancy will be less than years.

The probability that the mean life expectancy of the sample is less than X years is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean life expectancy, $\sigma$ is the standard deviation and n is the size of the sample.

8 0

2 years ago

What are the solution(s) to the quadratic equation 9x^2=4?

Irina18 [472]

Answer:

x = 2/3 or x = -2/3

Step-by-step explanation:

Solve for x over the real numbers:

9 x^2 = 4

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides by 9:

x^2 = 4/9

Hint: | Eliminate the exponent on the left-hand side.

Take the square root of both sides:

Answer:x = 2/3 or x = -2/3

8 0

3 years ago

Give the slope of each line. Also, state if the lines are parallel (yes or no).

VMariaS [17]

Answer:

AB slope is 1/2

CD slope is 1/3

Since the slopes of the lines aren't the same, the lines aren't parallel.

Step-by-step explanation:

5 0

2 years ago

Help! Will give crown to the most helping

kolbaska11 [484]

The first one seems more reasonable

8 0

2 years ago

-8(6-r)=24 what is the solution for r

Andreas93 [3]

Answer:hi

Step-by-step explanation:Let me first warn you that I CANNOT get the denominators of this problem to go underneath the numerators. It looks good on my answer page but when I click "preview your answer" the denominators are ALL over the place. Grrrrr.

I think the weirdly placed denominators make this explanation hard to understand but you give this a go and see if you understand things. If it is too hard to see, maybe this website will let you instant message me or email me. If so, then I will send you the solution via email. I'm very sorry the denominators are SO scattered.

See what you think of the explanations below but it might help if you write down my answer on paper, so that you can move the number to rest more closely under their proper numerators. :-)

Ok then......

Let's start with your first problem. A quick way to do this work is to cross multiply. Here's what I mean:

__3___ = __6___

r - 1 r + 2

Ok, so you can cross multiply:

3(r + 2) = 6(r - 1) (cross multiply)

3r + 6 = 6r - 6 (use the distributive property)

Now you will have to put the "r" variables on the left side of the equal sign and numbers without variables on the right side of the equal sign. To get 6r from the right side to the left, you can subtract 6r from the right side. If you subtract it from the right, you must subtract it from the left.....

To get 6 from the left side to the right, you can subtract it from the left. If you subtract it from the left, you must subtract it on the right.....

So now you have:

3r - 6r = -6 - 6 This becomes.........

- 3r = -12

Now to solve for "r" you will have to divide by -3. Why? Well, -3r is really saying: -3 times r. The -3 and the r are actually being multiplied together so to isolate the "r" you have to sort of "undo" the multiplication. What is the opposite of multiplication? It's DIVISION. Soooo, you must divide by -3 on both sides. SO you have:

- 3r = -12

r = 4 (-12 divided by -3 is a positive 4)

Now you know "r" equals 4. If we "plug" 4 back into the original equation, we can see the answer is correct. Check this out:

__3___ = __6___ (original equation)

r - 1 r + 2

__3___ = __6___ (substitute "4" in for "r"

4 - 1 4 + 2

__3___ = __6___ (do the math in the denominator area)

3 6

1 = 1 (3/3 equals 1 and 6/6 also equals 1, so our

solution that r = 4 is correct!) :-)

Now to your 2nd problem..........

4/2x-5 = 24/2x

___4___ = __24___

2x � 5 2x

Let's cross multiply again:

4(2x) = 24(2x - 5)

8x = 48x - 120

8x - 48x = - 120

-40x = - 120

(divide both sides by -40)

x = 3

Now let's "plug" 3 in where we had the variable "x" in the original equation to see if we are correct.

___4___ = __24___ (original equation)

2x � 5 2x

___4___ = __24___ (substituted 3 for "x")

2(3) � 5 2(3)

___4___ = __24___

6 - 5 6

___4___ = __24___

1 6

4 = 4

SO once again we have found the correct answer. Yay for us! :-)

I hope this helps. :-)

8 0

3 years ago

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