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In a National Achievement Test, Joshua obtained a score of 88. In the standardization of the test, μ = 78 and σ = 10. How would you communicate Joshua’s score to his parents? Explain your answer in writing

Respuesta :

Using the normal distribution, Joshua's score is communicated as being in the 84th percentile.

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 and the standard deviation are given by, respectively: [tex]\mu = 78, \sigma = 10[/tex].

He scored 88, hence X = 88 and his z-score is of:

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

[tex]Z = \frac{88 - 78}{10}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.84.

Hence, Joshua's score is communicated as being in the 84th percentile.

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

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