Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Answer:
a) The 36th percentile of the scores is of 74.68.
b) The 70th percentile of scores is 85.3.
c) The minimum score needed to get an A is 93.1.
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 of 79 and a standard deviation of 12.
This means that [tex]\mu = 79, \sigma = 12[/tex]
(a) Find the 36th percentile of the scores.
This is X when Z has a pvalue of 0.36. So X when Z = -0.36.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.36 = \frac{X - 79}{12}[/tex]
[tex]X - 79 = -0.36*12[/tex]
[tex]X = 74.68[/tex]
The 36th percentile of the scores is of 74.68.
(b) Find the 70th percentile of the scores.
This is X when Z has a pvalue of 0.7, so X when Z = 0.525.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.525 = \frac{X - 79}{12}[/tex]
[tex]X - 79 = 0.525*12[/tex]
[tex]X = 85.3[/tex]
The 70th percentile of scores is 85.3.
(c) The instructor wants to give an A to the students whose scores were in the top 12% of the class. What is the minimum score needed to get an A?
The 100 - 12 = 88th percentile, which is X when Z has a pvalue of 0.88, so X when Z = 1.175.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.175 = \frac{X - 79}{12}[/tex]
[tex]X - 79 = 1.175*12[/tex]
[tex]X = 93.1[/tex]
The minimum score needed to get an A is 93.1.
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
