Respuesta :
Answer:
Tanks of 15.3081 gallons and larger are considered too large.
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 = 15, \sigma = 0.15[/tex]
How large does a tank have to be to be considered too large
largest 2%, so at least the 98th percentile.
The 98th percentile is X when Z = 0.98. So it is X when Z = 2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.054 = \frac{X - 15}{0.15}[/tex]
[tex]X - 15 = 2.054*0.15[/tex]
[tex]X = 15.3081[/tex]
Tanks of 15.3081 gallons and larger are considered too large.
