   Chapter 9.3, Problem 36E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding Probabilities In Exercises 35 and 36, let x be a random variable that is normally distributed with the given mean and standard deviation. Find each probability using a symbolic integration utility. µ =   70 ,   σ =   14 ( a ) P ( x >   65 )                 ( b ) P ( x <   98 ) ( c ) P ( 49   ≤   x ≤   70 )       ( d ) P ( 56 <   x   <   75 )

(a)

To determine

To calculate: The probability P(x>65) by using a symbolic integration utility.

Explanation

Given information:

The provided mean is μ=70 and the standard deviation is σ=14.

Formula used:

The normal probability density function is given by,

f(x)=1σ2πe(xμ)2/(2σ2)

Where, μ is a mean and σ is standard deviation with random variable x in the interval <x<.

To find the probability,

P(axb)=abf(x)dx

Where, f is a probability density function with a continuous random variable x in the interval [a,b].

Calculation:

The normal probability density function as,

f(x)=1σ2πe(xμ)2/(2σ2)

Now substitute μ=70 and σ=14 in the above function,

f(x)=1142πe(x70)2/2(142)

Now apply the formula P(axb)=abf(x)dx

(b)

To determine

To calculate: The probability P(x<98) by using a symbolic integration utility.

(c)

To determine

To calculate: The probability P(49x70) by using a symbolic integration utility.

(d)

To determine

To calculate: The probability P(56<x<75) by using a symbolic integration utility.

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