Using the normal distribution, it is found that approximately 80% of the eggs on the farm have a mass greater than 51.5 g.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
[tex]\mu = 55, \sigma = 4.2[/tex].
Approximately 80% of the eggs on the farm have a mass greater than the 20th percentile, which is X when Z = -0.84, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 55}{4.2}[/tex]
X - 55 = -0.84 x 4.2
X = 51.5 g.
More can be learned about the normal distribution at https://brainly.com/question/24663213
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