Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
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
#SPJ4
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.