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HW5 - Conditional Probability (~2-day assignment)

Last updated almost 4 years ago
16 questions
Note from the author:
Mean and Standard Deviation Calculator.
Mean and Standard Deviation Calculator.
1

For this assignment, unless otherwise stated...

The number and type of animal at an animal shelter are shown in the diagram below.

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If an animal from the shelter is selected at random and is a cat, what is the probability that the cat has golden eyes?

P(eyes | cat)?

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If an animal from the shelter is selected at random and is a cat, what is the probability that the cat is a kitten?

P(kitten | cat)?

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Are golden eyes and type of animal independent or dependent traits?

The figure below represents a population. The population can have trait 1, trait 2, or both.
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Which area best describes the portion of the population with both traits?

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Which area best describes the portion of the population with either Trait 1 or Trait 2?

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Which area best describes the portion of the population with only trait 2, not trait 1?

A certain TV show has good guys and bad guys. Some characters have magical abilities, others are normal. The data is given in the table below.
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A character is selected at random and turns out to be a good guy. What is the probability that (s)he is a magic user?

P(magic | good)?

Enter your answer as a percent. Your answer should be an integer.

1

Which are true based on the data?

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Are good/bad and magical ability independent or dependent events?

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Give an example of a real-world situation that involves conditional probability. Include what the population/sample space is, what two events are involved, and how you expect the conditional probability to work (does one event make the other more likely, or less likely?).

Write your answer in standard English sentences. You will receive points for each of the three parts asked for.

1

Review:
Categorize each description with the type of study it describes.

  • involves a researcher dividing a population into multiple groups, giving each different treatments, and measuring the resulting differences.
  • involves a researcher asking a randomly selected sample the same set of questions
  • involves a reasearcher measuring and/or making notes on a sample of the population
  • a movie critic counts the number of male and female characters in the blockbuster and compares them
  • a producer asks a test audience how they liked the movie
  • a group is separated into two movie theaters. One subgroup watches the original Justice League and the other watches the longer director's cut. An observer records how many audience members fall asleep or leave the theater.
  • experiment
  • sample survey
  • observational study
Review:
Use the data below to answer the following questions.



1

What is the mean of the data?

Enter your answer as a number rounded to the nearest tenth.

1

What is the standard deviation of this data?

Enter your answer as a number rounded to the nearest tenth. (One decimal place)

1

What is the z-score for a data value of 42?

Enter your answer as a number rounded to two decimal places.

1

According to the z-score, what percent of the data is below the value 42?

Give your answer as a number rounded to two decimal places.