Respuesta :
Answer:
a) 0.345
b) 0.005
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 100
Standard Deviation, σ = 0.3
We are given that the distribution of lengths of lumber is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(length greater than 100.12 inches)
P(x > 100.12)
[tex]P( x > 100.12) = P( z > \displaystyle\frac{100.12 - 100}{0.3}) = P(z > 0.4)[/tex]
[tex]= 1 - P(z \leq 0.4)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 100.12) = 1 - 0.655 = 0.345 = 34.5\%[/tex]
b) Standard error due to sampling:
[tex]\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{0.3}{\sqrt{41}} = 0.0468[/tex]
P(length greater than 100.12 inches for the sample)
P(x > 100.12)
[tex]P( x > 100.12) = P( z > \displaystyle\frac{100.12 - 100}{0.0468}) = P(z > 2.564)[/tex]
[tex]= 1 - P(z \leq 2.564)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 100.12) = 1 - 0.995 = 0.005[/tex]
