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the height of seaweed of all plants in a body of water are normally distributed with a mean of 10 cm and a standard deviation of 2 cm.use excel to find which length separates the lowest 30% of the means of the plant heights in a sampling distribution of sample size 15 from the highest 70%? round your answer to the nearest hundredth.

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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