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The weight of a bag of Brand A cookies is labeled as 3 ounces on the bag. However, the actual weights of the bags vary by a small amount. According to the packaging specifications, the weights are approximately normally distributed with a mean of 3.05 ounces and a standard deviation of 0.06 ounce. Select the number to complete the sentence. According to the specifications, approximately percent of the bags weigh 3.00 ounces or more​

Sagot :

Using the normal distribution, it is found that approximately 79.67% of the bags weigh 3.00 ounces or more​.

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 = 3.05, \sigma = 0.06[/tex]

The proportion of the bags that weigh 3.00 ounces or more​ is one subtracted by the p-value of Z when X = 3, hence:

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

[tex]Z = \frac{3 - 3.05}{0.06}[/tex]

Z = -0.83

Z = -0.83 has a p-value of 0.2033.

1 - 0.2033 = 0.7967 = 79.67%.

79.67% of the bags weigh 3.00 ounces or more​.

More can be learned about the normal distribution at https://brainly.com/question/27643290

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