Question

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.)

Answer 1

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  

    $P( Z < -1.0537 ) = 0.14601$

=>  $P( X < 20) =0.14601$