Respuesta :
Answer:
The largest standard deviation for the amount of cereal in a box is 0.3906.
Step-by-step explanation:
Problems of normally distributed samples can be 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 = 16[/tex]
The z-score of X = 16 has a pvalue of 0.1. So it is [tex]Z = -1.28[/tex]. Now we have to find the value of [tex]\sigma[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{16 - 16.5}{\sigma}[/tex]
[tex]-1.28\sigma = -0.5[/tex]
[tex]\sigma = 0.3906[/tex]
The largest standard deviation for the amount of cereal in a box is 0.3906.
