How much do american airline flight attendants make an hour

Asked by admin @ in Mathematics viewed by 371 People

The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of $29.81 per hour and a standard deviation of $9.31 per hour. What is the probability that the hourly pay of a randomly selected flight attendant:

a. Is between the mean and $35.00 per hour? (Round intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
b. Is more than $35.00 per hour? (Round intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
c. Is less than $20.00 per hour? (Round intermediate calculations to 2 decimal places and final answer to 4 decimal places.)

Answered by admin @


Answer:

a

P(29.81 < X < 35) = 0.21141

b

P( X > 35) =0.28859

c

 P( X < 20) =0.14601    

Step-by-step explanation:

From the question we are told that

    The mean is  \mu = \$29.81

    The standard deviation is \sigma = \$9.31

Generally the probability that the hourly pay of a randomly selected flight attendant  Is between the mean and $35.00 per hour is mathematically represented as

      P(29.81 < X < 35) = P( \frac{ 29.81 - 29.81 }{9.31} < \frac{x - \mu }{\sigma} < \frac{ 35 - 29.81 }{9.31} )

\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )

     P(29.81 < X < 35) = P( 0 < Z < 0.5575 )

=>   P(29.81 < X < 35) = P( Z < 0.5575) - P( Z < 0)

From the z table  the area under the normal curve to the left corresponding to  0 and  0.5575   is  

   P( Z < 0) =0.5

and

   P( Z < 0.5575) = 0.71141

=>   P(29.81 < X < 35) = 0.71141 - 0.5

=>   P(29.81 < X < 35) = 0.21141

Generally the probability that the hourly pay of a randomly selected flight attendant  Is more than $35.00 per hour is mathematically represented as

   P(X > 35) = P( \frac{x - \mu }{\sigma} > \frac{ 35 - 29.81 }{9.31} )

   P( X > 35) = P( Z > 0.5575 )

From the z table  the area under the normal curve to the right  corresponding to 0.5575   is  

    P( Z > 0.5575 ) = 0.28859

=>  P( X > 35) =0.28859

Generally the probability that the hourly pay of a randomly selected flight attendant Is less than $20.00 per hour is mathematically represented as

   P(X

   P( X < 20) = P( Z < -1.0537 )

From the z table  the area under the normal curve to the right  corresponding to -1.0537  is  

    P( Z < -1.0537 ) = 0.14601

=>  P( X < 20) =0.14601    


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