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Statistics / Elementary Statistics: A Step By Step Approach 9 / Chapter 6.1 / Problem 58EC

Elementary Statistics: A Step By Step Approach | 9th Edition | ISBN: 9780073534985 | Authors: Allan Bluman

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Graph by hand the standard normal distribution by using

Chapter 6, Problem 58EC

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QUESTION:

Graph by hand the standard normal distribution by using the formula derived in Exercise 57. Let \(\pi \approx 3.14\) and \(e \approx 2.718\). Use X values of \(-2,\ -1.5,\ -1,\ -0.5,\ 0,\ 0.5,\ 1,\ 1.5\), and \(2\). (Use a calculator to compute the y values.)

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QUESTION:

Graph by hand the standard normal distribution by using the formula derived in Exercise 57. Let \(\pi \approx 3.14\) and \(e \approx 2.718\). Use X values of \(-2,\ -1.5,\ -1,\ -0.5,\ 0,\ 0.5,\ 1,\ 1.5\), and \(2\). (Use a calculator to compute the y values.)

ANSWER:

Solution

Step 1 of 2

We have to graph the standard normal distribution values for the given values of x

The formula is $y$ = $\frac{e{\ }^{-X{\ }^{2}/2}}{\sqrt{2\Pi{}}}$

The given values are $\Pi{}\simeq{}3.14$

$e\simeq{}2.718$

Substitute the given values in the formula $y=$ $\frac{(2.718){\ }^{-X{\ }^{2}/2}}{\sqrt{2(3.14)}}$

The given $X=-2,-1.5,-1,-0.5,\ 0,\ 0.5,\ 1,\ 1.5,\ 2$

If $x=-2\$ then $y=$ $\frac{(2.718){\ }^{-(-2){\ }^{2}/2}}{\sqrt{2(3.14)}}$ =0.054

If $x=-1.5\$ then $y=$ $\frac{(2.718){\ }^{-(-1.5){\ }^{2}/2}}{\sqrt{2(3.14)}}$ =0.1296

If $x=-1.0\$ then $y=$ $\frac{(2.718){\ }^{-(-1){\ }^{2}/2}}{\sqrt{2(3.14)}}$ =0.242

If $x=-0.5\$ then $y=$ $\frac{(2.718){\ }^{-(-0.5){\ }^{2}/2}}{\sqrt{2(3.14)}}$ =0.3522

If $x=0\$ then $y=$ $\frac{(2.718){\ }^{0{\ }^{2}/2}}{\sqrt{2(3.14)}}$ =0.399

If $x=0.5\$ then $y=$ $\frac{(2.718){\ }^{-(0.5){\ }^{2}/2}}{\sqrt{2(3.14)}}$ =0.3522

If $x=1.0\$ then $y=$ $\frac{(2.718){\ }^{-(1){\ }^{2}/2}}{\sqrt{2(3.14)}}$ =0.242

If $x=1.5\$ then $y=$ $\frac{(2.718){\ }^{-(1.5){\ }^{2}/2}}{\sqrt{2(3.14)}}$ =0.1296

If $x=2\$ then $y=$ $\frac{(2.718){\ }^{-(2){\ }^{2}/2}}{\sqrt{2(3.14)}}$ =0.054

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