Respuesta :
Answer:
At most 9.12 joules should be required for the bottom 80% of bottled water
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 question, we have that:
[tex]\mu = 8.7, \sigma = 0.5[/tex]
How much energy should be required for the bottom 80% of bottled water?
At most the 80th percentile.
The 80th percentile is X when Z has a pvalue of 0.8. So it is X when Z = 0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.84 = \frac{X - 8.7}{0.5}[/tex]
[tex]X - 8.7 = 0.84*0.5[/tex]
[tex]X = 9.12[/tex]
At most 9.12 joules should be required for the bottom 80% of bottled water
