Respuesta :
Using the normal distribution, it is found that there is a 0.0228 = 2.28% probability that X will be smaller than 80.
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.
In this problem:
- The mean is of [tex]\mu = 100[/tex].
- The standard deviation is of [tex]\sigma = 10[/tex].
The probability that X will be smaller than 80 is the p-value of Z when X = 80, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 100}{10}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
0.0228 = 2.28% probability that X will be smaller than 80.
More can be learned about the normal distribution at https://brainly.com/question/24663213
