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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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Meteorology A meteorologist predicts that the amount of rainfall x (in inches) expected for a certain coastal community during a hurricane has the probability density function

f ( x )   = π 30 sin π x 15 ,      0 x 15

Find and interpret each probability.

( a ) P ( 0     x     10 ) ( b )   P ( 10     x     15 ) ( c )   P ( 0     x   <   5 ) ( d )   P ( 12     x     15 )

a)

To determine

To calculate: The probability for the range P(0x10) and also interpret the result when the prediction of a meteorologist about the amount of rainfall x which is expected for a certain coastal community during a hurricane has the probability density function,

f(x)=π30 sinπx15,   0x15

Explanation

Given Information:

A meteorologist gives prediction about the amount of rainfall x which is expected for a certain coastal community during a hurricane has the probability density function,

f(x)=π30 sinπx15,   0x15

Formula used:

In a probability density function, the probability that x lies in interval [c,d] is given by,

P(cxd)=cdf(x) dx,

Which is shown in the figure below,

Calculation:

Consider the exponential probability density function,

f(x)=π30 sinπx15,   0x15

In order to calculate the probability for the range P(0x10) years integrate f(x) over interval [0,10]

b)

To determine

To calculate: The probability for the range P(10x15) and also interpret the result when the prediction of a meteorologist about the amount of rainfall x which is expected for a certain coastal community during a hurricane has the probability density function,

f(x)=π30 sinπx15,   0x15

c)

To determine

To calculate: The probability for the range P(0x<5) and also interpret the result when the prediction of a meteorologist about the amount of rainfall x which is expected for a certain coastal community during a hurricane has the probability density function,

f(x)=π30 sinπx15,   0x15

d)

To determine

To calculate: The probability for the range P(12x15) and also interpret the result when the prediction of a meteorologist about the amount of rainfall x which is expected for a certain coastal community during a hurricane has the probability density function,

f(x)=π30 sinπx15,   0x15

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