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Question

Graph by hand the standard normal distribution by using the formula derived in the Previous Exercise. 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.)

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 2Let $y$ be the value of the standard normal distribution function for any given $X$.

Using a calculator and the formula

$y=\frac{e^{-{\frac{X^2}2}}}{\sqrt{2\pi}}$

we calculate $y$ for each given value of $X$.

$X$ | $y$ |
---|---|

$-2$ | $0.05399$ |

$-1.5$ | $0.12951$ |

$-1$ | $0.24197$ |

$-0.5$ | $0.35206$ |

$0$ | $0.39894$ |

$0.5$ | $0.35206$ |

$1$ | $0.24197$ |

$1.5$ | $0.12951$ |

$2$ | $0.05399$ |

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