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Natali [406]
3 years ago
7

For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of sco

res that area. significantly high (or at least 2 standard deviations above the mean).b. significantly low (or at least 2 standard deviations below the mean).c.
Mathematics
1 answer:
Alex787 [66]3 years ago
6 0

Answer:

a) P(Z>2)

For this case we can use the normal standard table or excel and the complement rule and we got:

P(Z>2) =1-P(Z

b) P(Z

For this case we can use the normal standard table or excel and we got:

P(Z

c) P(-2

And we can find this probability with this difference:

P(-2

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let Z the random variable that represent the bone density scores of a population, and for this case we know the distribution for X is given by:

Z \sim N(0,1)  

Where \mu=0 and \sigma=1

We are interested on this probability

P(Z>2)

For this case we can use the normal standard table or excel and the complement rule and we got:

P(Z>2) =1-P(Z

Part b

We are interested on this probability

P(Z

For this case we can use the normal standard table or excel and we got:

P(Z

Part c: not significant​ (or less than 2 standard deviations away from the​ mean).

For this case we want this probability:

P(-2

And we can find this probability with this difference:

P(-2

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Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. Whe
kherson [118]

Answer:

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}  

n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11  

And rounded up we have that n=1068

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.03 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)

We don't have a prior estimation for the proportion \hat p so we can use 0.5 as an approximation for this case  

And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11  

And rounded up we have that n=1068

5 0
3 years ago
HELPP MEEEEEEEEE PLEASE
katrin [286]

Answer:

i think its A but im not sure

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Answer:

x = - 1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

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Answer:

8.5

Step-by-step explanation:

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Answer:

Ella grew \frac{1}{12} of an inch more

Step-by-step explanation:

For this problem, you want to subtract Ben's growth from Ella's.

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**This content involves adding and subtracting fractions, which you may want to revise. I'm always happy to help!

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