Respuesta :
Answer:
C. 3.2786 grams
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 = 74[/tex]
11% of the tomatoes are too small.
This means that when X = 70, Z has a pvalue of 0.11. So Z = -1.22.
Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.22 = \frac{70-74}{\sigma}[/tex]
[tex]-1.22\sigma = -4[/tex]
[tex]1.22\sigma = 4[/tex]
[tex]\sigma = \frac{4}{1.22}[/tex]
[tex]\sigma = 3.2786[/tex]
So the correct answer is:
C. 3.2786 grams
