Respuesta :
Using the normal distribution, it is found that 0.6826 = 68.26% of the subs that are sold are between 11.5 and 12.5 centimeters in length.
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 average length is of 12 inches, hence [tex]\mu = 12[/tex].
- The standard deviation is of 0.5 inches, hence [tex]\sigma = 0.5[/tex].
The proportion of the subs that are sold are between 11.5 and 12.5 centimeters in length is the p-value of Z when X = 12.5 subtracted by the p-value of Z when X = 11.5, hence:
X = 12.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12.5 - 12}{0.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
X = 11.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{11.5 - 12}{0.5}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
0.8413 - 0.1587 = 0.6826
0.6826 = 68.26% of the subs that are sold are between 11.5 and 12.5 centimeters in length.
To learn more about the normal distribution, you can take a look at https://brainly.com/question/24663213
