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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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 =  50 ,   σ =   10

( a ) P ( x >  5 5 )                 ( b ) P ( x <  60 ) ( c ) P ( 20     x  6 0 )       ( d ) P ( 30 <   x   <  5 5 )

(a)

To determine

To calculate: The probability P(x>55) by using a symbolic integration utility.

Explanation

Given information:

The provided mean is μ=50 and the standard deviation is σ=10.

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=50 and σ=10 in the above function,

f(x)=1102πe(x50)2/2(102)

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

(b)

To determine

To calculate: The probability P(x<60) by using a symbolic integration utility.

(c)

To determine

To calculate: The probability P(20x60) by using a symbolic integration utility.

(d)

To determine

To calculate: The probability P(30<x<55) by using a symbolic integration utility.

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