Answer :
Answer:
79.91% of loaves are between 26.94 and 32.18 centimeters
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 30, \sigma = 2[/tex]
What percentage of loaves are between 26.94 and 32.18 centimeters
This is the pvalue of Z when X = 32.18 subtracted by the pvalue of Z when X = 26.94.
X = 32.18:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32.18 - 30}{2}[/tex]
[tex]Z = 1.09[/tex]
[tex]Z = 1.09[/tex] has a pvalue of 0.8621
X = 26.94:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{26.94 - 30}{2}[/tex]
[tex]Z = -1.53[/tex]
[tex]Z = -1.53[/tex] has a pvalue of 0.0630
0.8621 - 0.0630 = 0.7991
79.91% of loaves are between 26.94 and 32.18 centimeters