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StatisticsQ&A LibraryA variable x of a finite population has the following frequency distribution:x578f254060Suppose a member is selected at random from the population and let X denote the value of the variable x for the member obtained.a. Determine the probability distribution of the random variable X.b. Use random-variable notation to describe the events that X takes on the value 6, a value of at most 6, and a value greater than 6.c. Find P(X = 6), P(X ≤ 6), and P(X >6). Interpret your results.d. Construct a probability histogram for the random variable X.Question

Asked Jan 21, 2020

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A variable x of a finite population has the following frequency distribution:

x | 5 | 7 | 8 |

f | 25 | 40 | 60 |

Suppose a member is selected at random from the population and let X denote the value of the variable x for the member obtained.

a. Determine the probability distribution of the random variable X.

b. Use random-variable notation to describe the events that X takes on the value 6, a value of at most 6, and a value greater than 6.

c. Find P(X = 6), P(X ≤ 6), and P(X >6). Interpret your results.

d. Construct a probability histogram for the random variable X.

Step 1

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Obtain the probability distribution for the random variable *X*:

The corresponding probabilities of the random variable *Y *is obtained by dividing frequency (*f*) of the random variable *X*, by total frequency (*N*).

That is,

Step 2

Total frequency is,

Step 3

The probability distribution for the random varia...

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