Answer:
a
[tex]P(29.81 < X < 35) = 0.21141[/tex]
b
[tex]P( X > 35) =0.28859[/tex]
c
[tex]P( X < 20) =0.14601[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = \$29.81[/tex]
The standard deviation is [tex]\sigma = \$9.31[/tex]
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
[tex]P(29.81 < X < 35) = P( \frac{ 29.81 - 29.81 }{9.31} < \frac{x - \mu }{\sigma} < \frac{ 35 - 29.81 }{9.31} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(29.81 < X < 35) = P( 0 < Z < 0.5575 )[/tex]
=> [tex]P(29.81 < X < 35) = P( Z < 0.5575) - P( Z < 0)[/tex]
From the z table the area under the normal curve to the left corresponding to 0 and 0.5575 is
[tex]P( Z < 0) =0.5[/tex]
and
[tex]P( Z < 0.5575) = 0.71141[/tex]
=> [tex]P(29.81 < X < 35) = 0.71141 - 0.5[/tex]
=> [tex]P(29.81 < X < 35) = 0.21141[/tex]
Generally the probability that the hourly pay of a randomly selected flight attendant Is more than $35.00 per hour is mathematically represented as
[tex]P(X > 35) = P( \frac{x - \mu }{\sigma} > \frac{ 35 - 29.81 }{9.31} )[/tex]
[tex]P( X > 35) = P( Z > 0.5575 )[/tex]
From the z table the area under the normal curve to the right corresponding to 0.5575 is
[tex]P( Z > 0.5575 ) = 0.28859[/tex]
=> [tex]P( X > 35) =0.28859[/tex]
Generally the probability that the hourly pay of a randomly selected flight attendant Is less than $20.00 per hour is mathematically represented as
[tex]P(X <20 ) = P( \frac{x - \mu }{\sigma} < \frac{20 - 29.81 }{9.31} )[/tex]
[tex]P( X < 20) = P( Z < -1.0537 )[/tex]
From the z table the area under the normal curve to the right corresponding to -1.0537 is
[tex]P( Z < -1.0537 ) = 0.14601[/tex]
=> [tex]P( X < 20) =0.14601[/tex]
