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Let random variable x represent the number of movies screening at movie theaters in a certain city. The following table shows the cumulative probability distribution of the discrete random variable X.

Andromeda claims the distribution of X is skewed to the right with a mean equal to 4 movies. Is Andromeda’s claim supported by the table.

A. Yes the distribution is skewed to the right with mean equal to four movies

B. No the distribution is skewed to the left with mean greater than 4 movies

C. No, the distribution is skewed to the left with mean less than 4 movies.

D. No, the distribution is skewed to the right with mean greater than 4 movies.

E. No, the distribution is skewed to the right with mean less than 4 movies.

Please help Let random variable x represent the number of movies screening at movie theaters in a certain city The following table shows the cumulative probabil class=

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lycasey16

Answer:

E. No, the distribution is skewed to the right with mean less than 4 movies.

Step-by-step explanation:

since this is the cumulative probability, you have to find the difference between each P(X≤x) value.  so the values go: 0.2, 0.3, and the rest are all 0.1

when you put that all into the calculator, the mean is 3.3 and when you graph it, the peak will be at x=2 and it will be skewed right

Using the cumulative distribution table, it is found that the correct option is:

E. No, the distribution is skewed to the right with mean less than 4 movies.

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From the table, the distribution is:

[tex]P(X = 1) = 0.2[/tex]

[tex]P(X = 2) = 0.3[/tex]

The above is because:

[tex]P(X \leq 2) = 0.5[/tex]

[tex]P(X \leq 1) + P(X = 2) = 0.5[/tex]

[tex]0.2 + P(X = 2) = 0.5[/tex]

[tex]P(X = 2) = 0.3[/tex]

Applying the same for the other values:

[tex]P(X = 3) = 0.1[/tex]

[tex]P(X = 4) = 0.1[/tex]

[tex]P(X = 5) = 0.1[/tex]

[tex]P(X = 6) = 0.1[/tex]

[tex]P(X = 7) = 0.1[/tex]

The expected value is each value multiplied by it's probability, so:

[tex]E(X) = 1(0.2) + 2(0.3) + 3(0.1) + 4(0.1) + 5(0.1) + 6(0.1) + 7(0.1) = 3.3[/tex]

  • The mean is 3.3, less than 4.
  • At least 60% of the values are below the mean, thus, the distribution is right-skewed, which means that the correct option is:

E. No, the distribution is skewed to the right with mean less than 4 movies.

A similar problem is given at https://brainly.com/question/16914931

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