Question

If a teacher gives a quiz that is normally distributed and has a mean score 50 and a standard deviation of 5:
a) what z score is associated with a 60th percentile
b) what score is associated with the 60th percentile

Answer 1

Using the normal distribution, it is found that:

a) The z-score associated with a 60th percentile score is of Z = 0.253.

b) The score associated with the 60th percentile is of 51.265.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• 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:

$\mu = 50, \sigma = 5$

The 60th percentile is X when Z has a p-value of 0.6, so X when Z = 0.253, hence:

$Z = \frac{X - \mu}{\sigma}$

$0.253 = \frac{X - 50}{5}$

X - 50 = 5(0.253)

X = 51.265.

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

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