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Exam 4: The Normal Distributions

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Question 21

Multiple Choice

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Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to Z > -1.62 is:

A) 0.0044.
B) 0.0526.
C) 0.9474.
D) 0.9956.

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Question 22

Multiple Choice

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The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with  = 100 and  =15. If you scored 130, your score would be higher than approximately what percent of adults?

A) 92%
B) 95%
C) 97.5%
D) 99.7%

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Question 23

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Scores on a university exam are Normally distributed, with a mean of 78 and a standard deviation of 8. The professor teaching the class declares that a score of 70 or higher is required for a grade of at least C. Using the 68-95-99.7 rule, what percent of students score below 62?

A high-profile consulting company chooses its new entry-level employees from a pool of recent college graduates using a five-step interview process. Unfortunately, there are usually more candidates who complete the interview process than the number of new positions that are available. As a result, cumulative GPA is used as a tie-breaker. GPAs for the successful interviewees are Normally distributed, with a mean of 3.3 and a standard deviation of 0.4. What proportion of candidates have a GPA under 3.0?

A Normal distribution:

The duration (in days) of human pregnancies follows approximately the N(266,16) distribution. What proportion of pregnancy durations is more than 270 days?

The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with  = 100 and  = 15. The proportion of adults with scores above 110 is closest to:

Scores on a university exam are Normally distributed, with a mean of 78 and a standard deviation of 8. The professor teaching the class declares that a score of 70 or higher is required for a grade of at least C. Using the 68-95-99.7 rule, what percent of students failed to earn a grade of at least C?

Birth weights at a local hospital have a Normal distribution, with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birth weights above 125 oz is:

Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to -0.5 < Z < 1.2 is:

You recently took a statistics exam in a large class. The instructor tells the class that the scores were Normally distributed, with a mean of 72 (out of 100) and a standard deviation of 12. Your score was 90. Your friend had a time conflict and took a course with another instructor. Your friend had a score of 75 on a test, with a mean of 60 and a standard deviation of 10. What can you conclude?

The duration (in days) of human pregnancies follows approximately the N(266, 16) distribution. How many days would a human pregnancy need to last to be among the top 10% of all pregnancy durations?

Scores on the SAT verbal test in recent years follow approximately the N(515, 109) distribution. How high must a student score in order to place in the top 5% of all students taking the SAT?

The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with  = 100 and  = 15. The proportion of adults with scores between 80 and 120 is closest to:

You recently took a statistics exam in a large class with n = 500 students. The instructor tells the class that the scores were Normally distributed, with a mean of 72 (out of 100) and a standard deviation of 8, but when you talk to other students in the class, you find out that more than 30 students have scores below 45. That violates which rule for the Normal distribution?

Birth weights at a local hospital have a Normal distribution, with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birth weights between 125 oz and 140 oz is:

A high-profile consulting company chooses its new entry-level employees from a pool of recent college graduates using a five-step interview process. Unfortunately, there are usually more candidates who complete the interview process than the number of new positions that are available. As a result, cumulative GPA is used as a tie-breaker. GPAs for the successful interviewees are Normally distributed, with a mean of 3.3 and a standard deviation of 0.4. What percent of candidates have a GPA above 3.9?