Respuesta :
Answer:
15.25% probability that the bottle contains between 12.3 and 12.36 ounces.
Step-by-step explanation:
Problems of normally distributed samples are solved using 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 problem, we have that:
[tex]\mu = 12.4, \sigma = 0.04[/tex]
Find the probability that the bottle contains between 12.3 and 12.36 ounces.
This is the pvalue of Z when X = 12.36 subtracted by the pvalue of Z when X = 12.3
X = 12.36
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12.36 - 12.4}{0.04}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
X = 12.3
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12.3 - 12.4}{0.04}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062
0.1587 - 0.0062 = 0.1525
15.25% probability that the bottle contains between 12.3 and 12.36 ounces.
