Quiz on Normal Curves and Statistical Analysis in STA2023 - Prof. Patrick S. Murphy, Quizzes of Data Analysis & Statistical Methods

A quiz for the statistics and probability course sta2023, focusing on normal curves and statistical analysis. It includes various questions requiring calculations based on the empirical rule and normal distribution, such as finding areas under the curve, probabilities, and z-scores. Students are expected to provide detailed solutions and explanations.

Typology: Quizzes

Pre 2010

Uploaded on 08/03/2009

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Quiz #2 STA2023
Basic Normal Curves
Provide all of your answers/explanations/work in the spaces provided. However,
you may attach additional work if you want to. Write your quiz up with your name, date,
and the time and days that you attend the class. Show all work for full credit. Your
submitted quiz should be neat, clear and detailed. It should not be a rough draft. When
in doubt, include as much relevant, correct information pertaining to your answer as
possible. Remember, start early and seek out help if you “get stuck.” There are two
printed pages to this quiz.
1. (2 pts.) Using the Empirical Rule only, state the area under the Standard Normal
Curve between
1
and 1.
2. (3 pts.) Calculate P(z >
65.0
). Round your answers to four decimal places. Don’t
put down just the answer, i.e., show all work for full credit!
3. The mean number of hours American workers spend on the computer is 3.1 hours per
workday. Assume that the standard deviation is 0.5 hour and that the variable is
normally distributed.
a) (4 pts.) Clearly, with detail, and using appropriate labeling notation, sketch by
hand the distribution of hours that American workers spend on the computer per
weekday.
pf2

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Quiz #2 STA Basic Normal Curves

Provide all of your answers/explanations/work in the spaces provided. However, you may attach additional work if you want to. Write your quiz up with your name, date, and the time and days that you attend the class. Show all work for full credit. Your submitted quiz should be neat, clear and detailed. It should not be a rough draft. When in doubt, include as much relevant, correct information pertaining to your answer as possible. Remember, start early and seek out help if you “get stuck.” There are two printed pages to this quiz.

  1. (2 pts.) Using the Empirical Rule only , state the area under the Standard Normal Curve between − 1 and 1.
  2. (3 pts.) Calculate P(z > − 0. 65 ). Round your answers to four decimal places. Don’t put down just the answer, i.e., show all work for full credit!
  3. The mean number of hours American workers spend on the computer is 3.1 hours per workday. Assume that the standard deviation is 0.5 hour and that the variable is normally distributed.

a) (4 pts.) Clearly, with detail, and using appropriate labeling notation , sketch by hand the distribution of hours that American workers spend on the computer per weekday.

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  1. Continued Now use your calculator to answer the following questions. Round your answers to four decimal places. Don’t put down just answers, i.e., show all work for full credit!

b) (3 pts.) What percent of American workers spend between two to two and a half hours on the computer?

c) (3 pts.) What is the probability that a random worker spends 3.8 hours or less on the computer?

d) (4 pts.) How long does an American worker spend on a computer if his/her time is in the lowest 25 percent?

e) (3 pts.) What proportion of hours spent on the computer are greater than 5 hours?

f) (3 pts.) What is the z-score for a time of 141 minutes?