Respuesta :
Answer:
a) P(x = 110) = 0
[tex]P( x < 110) = 0.6915 = 69.15\%[/tex]
[tex]P( x \leq 110) = 0.6915 = 69.15\%[/tex]
b) [tex]P(109 > x > 111) = 1- 0.3413 = 0.6587 = 65.87\%[/tex]
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 109
Standard Deviation, σ = 2
We are given that the distribution of blood chloride concentration is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P( chloride concentration equals 110)
P(x = 110) = 0
Because in a continuous distribution probability at one point is always zero.
P(chloride concentration is less than 110)
[tex]P(x < 110) = P(z > \displaystyle\frac{110-109}{2}) = P(z < 0.5)[/tex]
Calculating the value from the standard normal table we have,
[tex]P( x < 110) = 0.6915 = 69.15\%[/tex]
P(chloride concentration is at-most 110)
[tex]P(x \leq 110) = P(z \leq \displaystyle\frac{110-109}{2}) = P(z < 0.5)[/tex]
Calculating the value from the standard normal table we have,
[tex]P( x \leq 110) = 0.6915 = 69.15\%[/tex]
b) P(chloride concentration differs from the mean by more than 1 standard deviation)
P( 109 > x > 111) = 1 - P( 109 < x < 111)
[tex]P(109 \leq x \leq 111) = P(\displaystyle\frac{109 - 109}{2} \leq z \leq \displaystyle\frac{111-109}{2}) = P(0 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < 0)\\= 0.3413 = 34.13\%[/tex]
[tex]P(109 > x > 111) = 1- 0.3413 = 0.6587 = 65.87\%[/tex]
Clearly, this probability depend on the values of μ and σ.
