Answer:
C. 34.15 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= 33, \sigma = 0.7[/tex]
How heavy does a box have to be for it to be labeled overweight?
Top 5%, so X when Z has a pvalue of 1-0.05 = 0.95.
So X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 33}{0.7}[/tex]
[tex]X - 33 = 0.7*1.645[/tex]
[tex]X = 34.15[/tex]
So the correct answer is:
C. 34.15 oz
