Question

Determine the area under the standard normal curve that lies to the left of (a) Z=081. (b) Z=0.43. (c) Z= -0.33. and (d) Z= 1.04.

Answer 1

Using the normal distribution, the areas to the left are given as follows:

a) 0.7910.

b) 0.6664.

c) 0.3707.

d) 0.8508.

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, and is also the area to the left of Z.

Hence:

• The area to the left of Z = 0.81 is of 0.7910.

• The area to the left of Z = 0.43 is of 0.6664.

• The area to the left of Z = -0.33 is of 0.3707.

• The area to the left of Z = 1.04 is of 0.8508.

More can be learned about the normal distribution at brainly.com/question/4079902

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