Respuesta :
The value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
A normal distribution has symmetrically distributed data that is skew-free. As one proceeds away from the center, values tend to decrease and tend to cluster more frequently in that area. The mean, mode, and median of a normal distribution are all equal measures of central tendency.
Given data:
X: height of seaweed.
X~N (μ;σ²)
μ= 10 cm
σ= 2 cm
We will calculate the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70
P(X ≤ x) = 0.30
P(X ≥ x) = 0.70
Now by using the standard normal distribution,
we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula
[tex]Z = \frac{X-\mu}{\sigma}[/tex]
translates the Z value to the corresponding X value.
P(Z ≤ z) = 0.30
In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.
z= -0.52
Now you have to clear the value of X:
[tex]Z = \frac{X-\mu}{\sigma}[/tex]
X= (Z * σ) + μ
X = (-0.52 * 2)
= 8.96
hence, the value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
To learn more about normal distribution, visit the link below:
brainly.com/question/29433664
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