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Flashcards: Fitting Data Sets to Normal Distribution and Estimating Area Under the Curve: CCSS.Math.Content.HSS-ID.A.4

Suppose that the population of a certain city is normally distributed with a mean of 10 million people and a standard deviation of 4 million people. What is the probability that the current population is between 8 million and 12 million people?

34.13%

23.47%

75%

68.26%

50%

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Flashcards: Fitting Data Sets to Normal Distribution and Estimating Area Under the Curve: CCSS.Math.Content.HSS-ID.A.4

Your answer:

34.13%

Your answer:

23.47%

Your answer:

75%

Your answer:

50%

Correct answer:

68.26%

Explanation:

Flashcards: Fitting Data Sets to Normal Distribution and Estimating Area Under the Curve: CCSS.Math.Content.HSS-ID.A.4

A social scientist performs an experiment testing the frequency and correlation of several demographics. She plots a histogram measuring income versus education level. She produces the following model:

Negativenorm

Which of the following choices best describes this model?

None of these

Normal distribution

Positive/right skewed distribution

Negative/left skewed distribution

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Flashcards: Fitting Data Sets to Normal Distribution and Estimating Area Under the Curve: CCSS.Math.Content.HSS-ID.A.4

Negativenorm

Which of the following choices best describes this model?

Your answer:

Normal distribution

Your answer:

Positive/right skewed distribution

Your answer:

Negative/left skewed distribution

Correct answer:

None of these

Explanation:

In order to solve this problem let's review the following distributions: normal, positive/right skewed, negative/left skewed, bimodal, and uniform.

Normal Distribution:

Normal

A normal distribution is also known as a bell curve. Data that form a bell curve have three primary characteristics: the data is single peaked meaning that it has a single mode, it is symmetrical, and contains no outliers.

Positive/Right Skewed Distribution

Skewedright

A positive or right skewed distribution has a longer tail on the right side due to outliers while the majority of the points are concentrated on the left side of the graph. In other words, the set favors probabilities on the left of the model.

Negative/Left Skewed Distribution

Skewedleft

A negative or left skewed distribution has a longer tail on the left side due to outliers while the majority of the points are concentrated on the right side of the graph. In other words, the set favors probabilities on the right of the model.

Bimodal Distribution

Bimodal

In a bimodal distribution, there are two peaks due to several modes in the data set. These multiple central tendencies are the result of two or more favorable probabilities in the set.

Uniform Distribution

Uniform

In a uniform distribution the data points form a a rectangle. These models are formed when data points possess a constant probability.

The model in the question does not match any of these; therefore, the correct answer is "none of these."

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All Common Core: High School - Statistics and Probability Resources

Flashcards: Fitting Data Sets to Normal Distribution and Estimating Area Under the Curve: CCSS.Math.Content.HSS-ID.A.4

Flashcards: Fitting Data Sets to Normal Distribution and Estimating Area Under the Curve: CCSS.Math.Content.HSS-ID.A.4

Flashcards: Fitting Data Sets to Normal Distribution and Estimating Area Under the Curve: CCSS.Math.Content.HSS-ID.A.4

Flashcards: Fitting Data Sets to Normal Distribution and Estimating Area Under the Curve: CCSS.Math.Content.HSS-ID.A.4

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