Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Answer:
a = 200 + 0.253 * 50 = 212.65
So the value of height that separates the bottom 60% of data from the top 40% is 212.65. And rounded would be 212.
Step-by-Step Explanation:
The normal distribution is a "probability distribution that is symmetric around the mean, demonstrating that data near the mean occur more frequently than data distant from the mean."
The Z-score is defined as "a numerical measurement used in statistics of a value's relationship to the mean (average) of a set of values, expressed in standard deviations from the mean."
Let X be the random variable that represents how a loan officer scores credit applications from a population, and we know that the distribution for X is provided by:
X ~ N (200,50)
Where u = 200 and o = 50
And the best way to solve this problem is using the normal standard distribution and the z score given by:
Z = x - u/o
For this part we want to find a value a, such that we satisfy this condition:
P (X > a) = 0.40 (a)
P (X<a) = 0.60 (b)
In this example, both conditions are equal.
The z value that meets the criterion with 0.60 of the area on the left and 0.40 of the area on the right is z=0.253, as shown in the attached figure. P(Z0.253)=0.60 and P(z>0.253)=0.4 in this scenario.
Using the prior condition (b), we get:
P (X < a) = P (X-u/a < a - u/o) = 0.6
P (Z < a-u/o) = 0.6
But we know which value of z satisfy the previous equation so then we can do this:
z = 0.253 < a -200/50
And if we solve for a we got
a = 200 + 0.253 * 50 = 212.65
So the value of height that separates the bottom 60% of data from the top 40% is 212.65. And rounded would be 212.7.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.