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According to the empirical (69-95-99.7) rule, if a random variable z has a standard normal distribution, then approximately 95%
of all values fall between z-scores of -2 and 2. Use the standard normal table or software to determine the precise positive value
of z such that 95% of the area under the standard normal density curve is between -z and z. If you use software, you may find
this list of manuals useful.Give the positive value of z precise to two decimal places.

Respuesta :

Using z-scores, it is found that the value of z is z = 1.96.

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Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], is given by:  

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

  • It measures how many standard deviations the measure is from the mean.
  • Each z-score has an associated p-value, which is the percentile.

  • The normal distribution is symmetric, which means that the middle 95% is between the 2.5th percentile and the 97.5th percentile.
  • The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
  • The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
  • Thus, the value of Z is 1.96.

A similar problem is given at https://brainly.com/question/16965597

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