Respuesta :
Answer:
a) 0.586
b) 0.846
c) We are more likely to select a sample of 22 woman with a mean height of 64.9 inches.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 64.4 inches
Standard Deviation, σ =2.3 inches
We are given that the distribution of height of woman is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(selecting 1 woman with a height less than 64.9 inches)
P(x < 64.9)
[tex]P( x < 64.9) = P( z < \displaystyle\frac{64.9 - 64.4}{2.3}) = P(z < 0.2173)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 64.9) = 0.586 = 58.6\%[/tex]
b) P(selecting 22 woman with a height less than 64.9 inches)
Standard error due to sampling =
[tex]\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{2.3}{\sqrt{22}} = 0.49[/tex]
P(x < 64.9)
[tex]P( x < 64.9) = P( z < \displaystyle\frac{64.9 - 64.4}{\frac{2.3}{\sqrt{22}}}) = P(z < 1.0196)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 64.9) = 0.846 = 84.6\%[/tex]
c) Since,
P(selecting 22 woman with a height less than 64.9 inches) > P(selecting 1 woman with a height less than 64.9 inches)
We are more likely to select a sample of 22 woman with a mean height of 64.9 inches.
