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14 August, 16:04

Let the random variable X be the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. The distribution for the units is given below.

X 3 4 5 6 7 8 9 10

P (X) 0.07 0.23 0.36 0.19 0.05 0.05 0.03?

(a) Is X a discrete or continuous random variable?

(b) What must be the probability of choosing a unit with 10 rooms?

(c) What is the probability that a unit chosen at random is not a 10-room unit?

(d) What is the probability that a unit chosen at random has less than five rooms?

(e) What is the probability that a unit chosen at random has three rooms?

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  1. 14 August, 17:07
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    a) X is a discrete random variable.

    b) 2% probability of choosing a unit with 10 rooms

    c) 98% probability that a unit chosen at random is not a 10-room unit

    d) 30% probability that a unit chosen at random has less than five rooms

    e) 7% probability that a unit chosen at random has less than five rooms

    Step-by-step explanation:

    The distribution means that:

    7% probability that a randomly chosen owner-occupied housing unit in a certain city has 3 rooms.

    23% probability that a randomly chosen owner-occupied housing unit in a certain city has 4 rooms.

    36% probability that a randomly chosen owner-occupied housing unit in a certain city has 5 rooms.

    19% probability that a randomly chosen owner-occupied housing unit in a certain city has 6 rooms.

    5% probability that a randomly chosen owner-occupied housing unit in a certain city has 7 rooms.

    5% probability that a randomly chosen owner-occupied housing unit in a certain city has 8 rooms.

    3% probability that a randomly chosen owner-occupied housing unit in a certain city has 9 rooms.

    ?% probability that a randomly chosen owner-occupied housing unit in a certain city has 10 rooms.

    (a) Is X a discrete or continuous random variable?

    X is the number of rooms in a randomly selected house. The number of rooms is a countable variable, that is, only assumes values like 1,2,3,4, ... You cannot have 3.5 rooms, for example.

    So X is a discrete random variable.

    (b) What must be the probability of choosing a unit with 10 rooms?

    The sum of all probabilities must be 100% (1 decimal). So

    0.07 + 0.23 + 0.36 + 0.19 + 0.05 + 0.05 + 0.03 + ? = 1

    0.98 + ? = 1

    ? = 0.02

    2% probability of choosing a unit with 10 rooms

    (c) What is the probability that a unit chosen at random is not a 10-room unit?

    0.07 + 0.23 + 0.36 + 0.19 + 0.05 + 0.05 + 0.03 = 0.98

    98% probability that a unit chosen at random is not a 10-room unit

    (d) What is the probability that a unit chosen at random has less than five rooms?

    7% probability it has 3 rooms

    23% probability it has 4 rooms. So

    7+23 = 30% probability that a unit chosen at random has less than five rooms

    (e) What is the probability that a unit chosen at random has three rooms?

    7% probability that a randomly chosen owner-occupied housing unit in a certain city has 3 rooms. So

    7% probability that a unit chosen at random has less than five rooms
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