Respuesta :
Answer:
a) 0.3413
b) 0.1587
c) 0.3341
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 20.50 dollars
Standard Deviation, σ = 3.50 dollars
We are given that the distribution of hourly wages is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(Between $20.50 and $24.00 per hour
[tex]P(20.50 \leq x \leq 24) = P(\displaystyle\frac{20.50 - 20.50}{3.50} \leq z \leq \displaystyle\frac{24-20.50}{3.50}) = P(0 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < 0)\\= 0.8413 - 0.5000 = 0.3413 = 34.13\%[/tex]
[tex]P(20.50 \leq x \leq 24) = 34.1\%[/tex]
b) P(More than $24.00 per hour)
P(x > 24)
[tex]P( x > 24) = P( z > \displaystyle\frac{24 - 20.50}{3.50}) = P(z > 1)[/tex]
[tex]= 1 - P(z \leq 1)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 610) = 1 - 0.8413 = 0.1587 = 15.87\%[/tex]
c) P(Less than $19.00 per hour)
P(x < 19)
[tex]P( x < 19) = P( z > \displaystyle\frac{19 - 20.50}{3.50}) = P(z < -0.4285)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 19) =0.3341= 33.41\%[/tex]
