EBook Problems Normal Critical

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EBook Problems Set - Nonstandard Normal Distribution: Finding Scores (Critical Values)

Problem 1

Given the following summary statitics, which of the statements below is true?

Chemistry test score of Class A: Mean = 70 Standard deviation = 10 Chemistry test score of Class B: Mean = 70 Standard deviation = 5

Jack is in class A and got a score of 80 John is in class B and got a score of 80

  • Choose one answer.
(a) John's performance in chemistry is better than Jack's.
(b) Jack and John did equally well in chemistry.
(c) John's and Jack's scores in chemistry are not comparable.
(d) We need more information to compare Jack's and John's scores.

Problem 2

A statistics professor teaches two different sections of the same class. To prevent cheating, the classes get different midterms. This year, the midterm for Section A had a mean of 60% with a standard deviation of 10%. The midterm for Section B had a mean of 65% and a standard deviation of 5%. Kefei scored 75% in Section A, while her friend Bob in Section B scored 75%. Grades on this midterm are based upon how each student does relative to the other students in his or her class.

Which of the following best describes the situation?

  • Choose one answer.
(a) Because the midterms contained different questions, we can't compare their performance.
(b) Relative to other classmates, both Bob and Kefei did equally well.
(c) Relative to other classmates, Bod did better on the exam than Kefei.
(d) Relative to other classmates, Kefei did better on the exam than Bob.

Problem 3

In Japan there is an annual turkey dog eating contest. The number of turkey dogs that contestants eat are normally distributed with a mean of 36 turkey dogs and a standard deviation of 6 turkey dogs. A contestant eats 27 turkey dogs. What is his z-score?

  • Choose one answer.
(a) 9
(b) 1.5
(c) 6
(d) -9
(e) -1.5

Problem 4

Volunteers from Heal the Bay determined that the lengths of individual shellfish in the population of 10,000 shellfish are nearly normal with mean 10 centimeters and deviation of 0.2 centimeters. Determine the shortest interval that contains approximately 4,000 shellfish.

  • Choose one answer.
(a) 9.744cm to 10cm
(b) 9.928cm to 10.080cm
(c) 0cm to 9.949cm
(d) 9.774cm to 10.256cm
(e) 9.895cm to 10.105cm

Problem 5

You read that the heights of college women are nearly normal with a mean of 65 inches and a standard deviation of 2 inches. If Vanessa is at the 10th percentile (shortest 10% for women) in height for college women, then her height is closest to:

  • Choose one answer.
(a) 64.5 inches
(b) It cannot be determined from this information
(c) 60.5 inches
(d) 62.44 inches

Problem 6

The length of human pregnancies from conception to birth has a distribution that is approximately normal, with a mean 266 days and a standard deviation of 16 days. How short are the shortest 4% of pregnancies?

  • Choose one answer.
(a) Less than 210 days
(b) Less than 266 days
(c) Less than 238 days
(d) Less than 280 days

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