Mathematics, 19.07.2019 16:30, lexieforlife911

For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are a. significantly high (or at least 2 standard deviations above the mean). b. significantly low (or at least 2 standard deviations below the mean). c. not significant (or less than 2 standard deviations away from the mean).

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answered: andrewmena05

Using the normal distribution, it is found that:

a) 2.28% of scores are significantly high.

b) 2.28% of scores are significantly low.

c) 95.44% of scores are not significant.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of both X and Z.

Item a:

The probability of finding a value at least 2 standard deviations above the mean is: $P(Z \geq 2)$ , which is 1 subtracted by the p-value of Z = 2.

Z = 2 has a p-value of 0.9772.

1 - 0.9772 = 0.0228

Then, 2.28% of scores are significantly high.

Item b:

The probability of finding a value at least 2 standard deviations below the mean is: $P(Z \leq -2)$ , which is the p-value of Z = 2.

Z = -2 has a p-value of 0.0228.

Then, 2.28% of scores are significantly low.

Item c:

The probability is $P(-2 \leq Z \leq 2)$ , which is the p-value of Z = 2 subtracted by the p-value of Z = -2.

Z = 2 has a p-value of 0.9772.

Z = -2 has a p-value of 0.0228.

Then, 95.44% of scores are not significant.

A similar problem is given at link

answered: emmanolan112

In a normal distribution 68.27% of the values are within one standard deviation from the mean, 95.5% of the values are within two standard deviations from the mean, and 99.7 % of the values are within three standard deviations of the mean

With that you have the answer to the three questions:

a. significantly high (or at least 2 standard deviations above the mean).

99.5% of the values are within 2 standard deviations from the mean, half of 100% - 95.5% = 4.5% / 2 = 2.25% are above the mean, so the answer is 2.25%

b. significantly low (or at least 2 standard deviations below the mean).

The other half are below 2 standard deviations, so the answer is 2.25%

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

As said, 95.5% are within the band of two standard deviations from the mean, so the answer is 95.5%.

answered: Guest

step-by-step explanation:

answered: Guest

answer: solve 5\cdot 2^x=2405⋅2

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}

5⋅2

=240

=48

step-by-step explanation: