Question

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1
z=0.65

Answer 1

Answer:

0.74215

Step-by-step explanation:

Given: Mean= 0

          Standard deviation= 1

          Z= 0.65

First lets find the z score of 0.65 from the normal distribution table.

∴ The value from the table is $0.74215$

Now using the formula for z-score to find x, which is the shaded region.

Z-score= $\frac{x-mean}{standard\ deviation}$

⇒ $0.74215= \frac{x-0}{1}$

Multiplying both side by 1

∴ $x= 0.74215$

Hence, the area of shaded region is 0.74215.

Answer 2

The area of the shaded region as depicted by the graph is 0.7422

The formula for calculating the z-score is expressed as:

$z=\frac{x-\mu}{\sigma}$

Given the following

$z=0.65\\\mu=0\\\sigma = 1$

The z-score of the distribution from the distribution table for z = 0.65 is 0.7422

Substituting the given values into the formula:

$0.7422=\frac{x-0}{1.0} \\Cross \ multiply\\0.7422 \times 1.0=x-0\\0.7422=x\\x=0.7422$

Hence the area of the shaded region as depicted by the graph is 0.7422

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