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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Answer from: 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

Answer from: 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%.

Answer from: Quest

true

step-by-step explanation:

Answer from: Quest

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities. if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.

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For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1...