Respuesta :
Answer: P(x > 170) = 0.04
Step-by-step explanation:
Since the the surface areas of the red blood cells in a typical blood sample have a normal distribution, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = surface areas of red blood cells.
µ = mean surface area
σ = standard deviation
From the information given,
µ = 135 µm2
σ = 20 µm2
We want to find the fraction of the red blood cells that has a surface area larger than 170 µm2. It is expressed as
P(x > 170) = 1 - P(x ≤ 170)
For x = 170,
z = (170 - 135)/20 = 1.75
Looking at the normal distribution table, the probability corresponding to the z score is 0.96
P(x > 170) = 1 - 0.96
P(x > 170) = 0.04
Answer:
Fraction of the red blood cells having a surface area larger than 170 [tex]\mu m^{2}[/tex] is 0.04006 or 4% .
Step-by-step explanation:
We are given that in a typical blood sample, the surface areas of the red blood cells have a normal distribution with a mean of 135 [tex]\mu m^{2}[/tex] and a standard deviation of 20 [tex]\mu m^{2}[/tex] .
Let X = the surface areas of the red blood cells, i.e;
X ~ N([tex]\mu = 135,\sigma^{2} = 20^{2}[/tex])
The Z score probability distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ Standard Normal(0,1)
So, fraction of the red blood cells having a surface area larger than 170 [tex]\mu m^{2}[/tex] is given by P(X > 170 [tex]\mu m^{2}[/tex] ) ;
P(X > 170) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{170-135}{20}[/tex] ) = P(Z > 1.75) = 1 - P(Z <= 1.75)
= 1 - 0.95994 = 0.04006 or approx 4%.
Therefore, approx 4% of the red blood cells has a surface area larger than 170 [tex]\mu m^{2}[/tex] .
