Respuesta :
Using the normal distribution, it is found that the statements are classified as:
1. False.
2. True.
3. False.
Normal Probability Distribution
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 X.
Item 1:
We have that [tex]\mu = 150, \sigma = 6, X = 120[/tex], hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 150}{6}[/tex]
[tex]Z = -5[/tex]
Hence the statement is false.
Item 2:
z = 2 has a p-value of 0.9772, z = -2 has a p-value of 0.0228.
0.9772 - 0.0228 = 0.9544.
Hence the statement is true.
Item 3:
The mean is 0 and the standard deviation is 1, hence the statement is false.
More can be learned about the normal distribution at https://brainly.com/question/24663213
