Respuesta :
Answer:
40.13% probability that the volume of soda in a randomly selected bottle will be less than 32 oz.
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 = 32.3, \sigma = 1.2[/tex]
What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?
This is the pvalue of Z when X = 32. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32 - 32.3}{1.2}[/tex]
[tex]Z = -0.25[/tex]
[tex]Z = -0.25[/tex] has a pvalue of 0.4013
40.13% probability that the volume of soda in a randomly selected bottle will be less than 32 oz.
