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Exam 6: The Normal Distribution

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Question 41

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Provide an appropriate response. Assume that the variable under consideration has a density curve. -The percentage of all possible observations of the variable that lie between 5 and 10 equals the area under its density curve between and , expressed as a percentage.

A) 0.05, 0.1
B) 5, 10
C) 6, 11
D) 2.5, 5

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Question 42

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Use a table of areas to find the specified area under the standard normal curve. -The area that lies to the left of 1.13

A) 0.8907
B) 0.8708
C) 0.1292
D) 0.8485

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Question 43

Multiple Choice

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Find the specified percentile, quartile, or decile. -At one college, GPAs are normally distributed with a mean of 2.8 and a standard deviation of 0.6. Find the third quartile, $\mathrm { Q } _ { 3 } .$

Find the specified percentile, quartile, or decile. -Scores on an English test are normally distributed with a mean of 32.7 and a standard deviation of 8.2. Find the 41st percentile.

Sketch a standard normal curve and shade the area between the z-scores -2.5 and -1.

According to data from the American Medical Association, 10% of us are left-handed. Suppose a group of 500 people is randomly selected. You wish to find the probability that at least 80 are left-handed. Describe the characteristics of this problem which help you to recognize that the problem is about a binomial distribution that you are to solve by estimating with the normal distribution. (Assume that you would not use a computer, a table, or the binomial probability formula.)

The area under the standard normal curve to the right of a z-score is 0.56. Explain how you could use a table of areas to find the z-score.

Provide an appropriate response. -Under what conditions are you allowed to use the normal distribution to approximate the binomial distribution? Under what conditions might you want to use the normal distribution to approximate the binomial as opposed to using the binomial probability formula, a table of binomial probabilities, or a computer?

Use a table of areas to obtain the shaded area under the standard normal curve. -

Areas under the standard normal curve cannot be negative, whereas z-scores can be positive or negative.

A normal probability plot is given below for a sample of scores on an aptitude test. Use the plot to assess the normality of scores on this test. Explain your reasoning.

Provide an appropriate response. -Which of the variables below do you think will be roughly normally distributed? a. Weights of 10 year old boys b. Incomes of 40 year old adults c. The numbers that show up when you roll a balanced die d. The amount of coffee which a filling machine puts into " 4 ounce jars"

Fill in the blanks by standardizing the normally distributed variable. -Dave drives to work each morning at about the same time. His commute time is normally distributed with a mean of 42 minutes and a standard deviation of 8 minutes. The percentage of Time that his commute time lies between 18 and 58 minutes is equal to the area under the standard Normal curve between ___ and ___.

Use a table of areas to obtain the shaded area under the standard normal curve. -

On the same axes sketch normal distributions with a. $\mu = 6 , \sigma = 4$ b. $\mu = 6 , \sigma = 2$ C. $\mu = - 6 , \sigma = 2$ .

Which is larger, the area under the standard normal curve between -1 and 1, or the area under the standard normal curve between 0 and 2? Explain your reasoning.

Use the empirical rule to solve the problem. -At one college, GPAs are normally distributed with a mean of 2.8 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.2 and 3.4?

Use a table of areas for the standard normal curve to find the required z-score. -Determine the two z-scores that divide the area under the standard normal curve into a middle 0.96 area and two outside 0.02 areas.

Use a table of areas to find the specified area under the standard normal curve. -The area that lies to the right of 0.59

Suppose that scores on a test are normally distributed with a mean of 80 and a standard deviation of 8. Read the two questions below. A. What is the 90th percentile? B. What percentage of students score less than 90? Explain the difference between the two questions. Describe how the method for solving A would differ from the the method for solving B. Be sure to include in your explanation a description of how the table of areas would be used in each case.