Question

math hw 1

The Normal Distribution


pls help me with my homework!!


thanks,

Answer 1

Using the normal distribution, it is found that the desired measures are given by:

a. Z = -0.67.

b. X = 2.2.

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.

In item a, we have that $X = 36, \mu = 40, \sigma = 6$, and want to find Z, hence:

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

$Z = \frac{36 - 40}{6}$

Z = -0.67.

In item b, we have that $\mu = 1.3, \sigma = 0.6, Z = 1.5$, and want to find X, hence:

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

$1.5 = \frac{X - 1.3}{0.6}$

X - 1.3 = 0.6 x 1.5

X = 2.2.

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

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