Explanation Given: The mean annual wage for firefighters is $50,000 with a standard deviation of $12,000. The normal probability density function is, f ( x ) = 1 σ 2 π e − ( x − μ ) 2 / 2 σ 2 where μ is the mean and σ is the standard deviation. Result used: If [ c , d ] is a subinterval of ( − ∞ , ∞ ) , then P ( c ≤ x ≤ d ) = ∫ c d f ( x ) d x , where f ( x ) is the normal probability density function of the continuous random variable X . Calculation: Substitute the given values μ = 50000 and σ = 12000 in the normal density function f ( x ) , f ( x ) = 1 12000 1 2 π e − ( x − 50000 ) 2 2 ( 12000 ) 2 = 1 12000 ⋅ 1 2 π e − ( x − 50000 ) 2 2 ( 144000000 ) = 1 12000 ⋅ 1 2 π e − ( x − 50000 ) 2 288000000 From the above mentioned result, obtain the probability that the fire fighter earns between $45000 and $65000 that is P ( 45000 ≤ X ≤ 65000 ) as follows

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Chapter 6.2, Problem 31E

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The probability that the firefighter earns between $ 45000 and $ 65000 .

Solution Summary: The author calculates the probability that a firefighter earns between 45000 and 65000.

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