Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Answer:
z = 1.28 < a - 200/20
And if we solve for a we got
a = 200 + 1.28 * 20 = 225.6
So the value of height that separates the bottom 90% of data from the top 10% is 225.6.
Step-by-step explanation:
Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:
X ~ N (200,20)
For u = 200 and o = 20
For this case we can use the z score in order to solve this problem, given by this formula:
Z = x-u/o
For this part we want to find a value a, such that we satisfy this condition:
P (X > a) = 0.1 (a)
P (X < a) = 0.9 (b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1
If we use condition (b) from previous we have this:
P ( X < a) = P (X-u/o < a - u/o) = 0.9
P (z < a-u/o) = 0.9
But we know which value of z satisfy the previous equation so then we can do this:
z = 1.28 < a - 200/20
And if we solve for a we got
a = 200 + 1.28 * 20 = 225.6
So the value of height that separates the bottom 90% of data from the top 10% is 225.6.
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.