Respuesta :
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%.
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%.
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- 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: [tex]P(Z \geq 2)[/tex], 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: [tex]P(Z \leq -2)[/tex], 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 [tex]P(-2 \leq Z \leq 2)[/tex], 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 https://brainly.com/question/13073931
