Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

The American Economic Review (December 2008) published a study on the factors (other than credit constraints) that would influence the college dropout decision. One factor of interest was expected GPA for a college student who studied 3 hours per day. In a representative sample of 307 college students, the researchers reported the following summary statistics for the expected GPA of those who studied 3 hours per day: x 3.11, s 66. a. Give an interval that will contain most (at least 75% to approximately 95%) of the 307 GPAs. b. If you observe a GPA of 1.25, is it likely that this college student studied 3 hours per day? Explain.

Sagot :

Using the normal distribution, it is found that:

a) The interval that will contain most of the GPA's is (1.79, 4.43).

b) The z-score associated with this grade is of -2.82 < -2, thus, it is unlikely that this student studied 3 hours per day.

-----------------

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.

  • If |Z| > 2, the measure X is considered to be unlikely.

-----------------

  • Mean of 3.11 means that [tex]\mu = 3.11[/tex]
  • Standard deviation of 0.66 means that [tex]\sigma = 0.66[/tex]

-----------------

Item a:

  • This interval is composed by measures within 2 standard deviations of the mean, thus:

[tex]3.11 - 2(0.66) = 1.79[/tex]

[tex]3.11 + 2(0.66) = 4.43[/tex]

The interval that will contain most of the GPA's is (1.79, 4.43).

-----------------

Item b:

We have to find the z-score when [tex]X = 1.25[/tex], thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1.25 - 3.11}{0.66}[/tex]

[tex]Z = -2.82[/tex]

The z-score associated with this grade is of -2.82 < -2, thus, it is unlikely that this student studied 3 hours per day.

A similar problem is given at https://brainly.com/question/16347292

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.