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Use technology or a z-distribution table to find the indicated area.

The masses of the eggs collected on a farm are normally distributed with a mean of 55 grams and a standard deviation of 4.2 grams.

Approximately 80% of the eggs on the farm have a mass greater than which mass?

51.5 g

54.1 g

55.8 g

58.5 g

Sagot :

Valantheamastacia

Answer:

51.5g or A

I took a test with this question and got it right

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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