Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Answer:
The middle 90% of all freshman biology majors' GPAs lie between 2.31 and 3.43.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean 2.87 and standard deviation .34.
This means that [tex]\mu = 2.87, \sigma = 0.34[/tex]
Middle 90% of scores:
Between the 50 - (90/2) = 5th percentile and the 50 + (90/2) = 95th percentile.
5th percentile:
X when Z has a pvalue of 0.05. So X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 2.87}{0.34}[/tex]
[tex]X - 2.87 = -1.645*0.34[/tex]
[tex]X = 2.31[/tex]
95th percentile:
X when Z has a pvalue of 0.95. So X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 2.87}{0.34}[/tex]
[tex]X - 2.87 = 1.645*0.34[/tex]
[tex]X = 3.43[/tex]
The middle 90% of all freshman biology majors' GPAs lie between 2.31 and 3.43.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
