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Zoey is participating in a contest where she may pick any random box filled with sausages for only $1. The number of sausages in boxes vary but are randomly distributed. If the average box contains 13 sausages with a standard deviation of 4 sausages. What is the probability of Zoey randomly selecting a box that has more than 19 sausages in it?

Respuesta :

Using the normal distribution, it is found that there is a 0.0668 = 6.68% probability of Zoey randomly selecting a box that has more than 19 sausages in it.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • It 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, which is the percentile of X

In this problem:

  • The mean is of [tex]\mu = 13[/tex].
  • The standard deviation is of [tex]\sigma = 4[/tex].

The probability of Zoey randomly selecting a box that has more than 19 sausages in it is 1 subtracted by the p-value of Z when X = 19, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{19 - 13}{4}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a p-value of 0.9332.

1 - 0.9332 = 0.0668.

0.0668 = 6.68% probability of Zoey randomly selecting a box that has more than 19 sausages in it.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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