Question

The following table provides a frequency distribution for the number of rooms in this country's housing units The frequencies are in thousands Rooms No. of units 561 2 1475 3 10.995 4 23,341 5 27.900 6 24,632 7 14650 8+ 17.211 a. Find the probability that the housing unit obtained has four rooms The probability is 0,193 (Round to three decimal places as needed.) b. Find the probability that the housing unit obtained has more than four rooms. The probability as (Round to three decimal places as needed.) A housing untis selected at random. Find the following probabies

Answer 1

The probability that a randomly selected housing unit has four rooms is approximately 0.0917, while the probability of having more than four rooms is around 0.9030 when rounded to four decimal places.

Step-by-step explanation:

The probability that a housing unit obtained has four rooms is calculated by dividing the frequency of units with four rooms by the total number of units. To find the total number of units, we add up the frequencies for all the room categories:

Total units = 561 + 1475 + 10,995 + 23,341 + 27,900 + 24,632 + 14,650 + 17,211 = 119,765 (in thousands).

Now, we calculate the probability of a housing unit having exactly four rooms:

P(four rooms) = Frequency of units with four rooms / Total number of units

P(four rooms) = 10,995 / 119,765 ≈ 0.0917 or 9.17%.

To calculate the probability that a housing unit obtained has more than four rooms, we add up the frequencies of all categories above four rooms and divide by the total number of units:

P(more than four rooms) = (23,341 + 27,900 + 24,632 + 14,650 + 17,211) / 119,765

P(more than four rooms) ≈ 0.9030 or 90.30% after rounding to four decimal places.