Respuesta :
Answer:
1164.5 gallons of milk.
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 = 1000, \sigma = 100[/tex]
How many gallons must be in stock at the beginning of the day if Gillis is to have only a 5% chance of running out of milk by the end of the day?
This is the value of X when Z has a pvalue of 1-0.05 = 0.95. So it is X when [tex]Z = 1.645[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 1000}{100}[/tex]
[tex]X - 1000 = 1.645*100[/tex]
[tex]X = 1164.5[/tex]
1164.5 gallons of milk.
