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) If the warranty guarantees the dishwasher will last at least 14 years or your money back, what is the probability that the company will have to refund money to a customer

Respuesta :

Using the normal distribution, it is found that there is a 0.6406 = 64.06% probability that the company will have to refund money to a customer.

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.

Researching the problem on the internet, it is found that the mean and the standard deviation are, respectively, given by [tex]\mu = 13[/tex] and [tex]\sigma = 2.75[/tex].

The probability it lasts less than 14 years is the p-value of Z when X = 14, hence:

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

[tex]Z = \frac{14 - 13}{2.75}[/tex]

[tex]Z = 0.36[/tex]

[tex]Z = 0.36[/tex] has a p-value of 0.6406.

0.6406 = 64.06% probability that the company will have to refund money to a customer.

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

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