Question

The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 35 hours and the median is 31.2 hours. Twenty-four of the families in the sample turned on the television for 20 hours or less for the week. The 12th percentile of the data is 20 hours. Step 1 of 5: Based on the given information, determine if the following statement is true or false. The 55th percentile is greater than or equal to 30 hours.
1: Approximately how many families are in the sample? Round your answer to the nearest integer.
2: Based on the given information, determine if the following statement is true or false. Approximately 200 families turned on their televisions for less than 35 hours.
3: What is the value of the 50th percentile?
4: Based on the given information, determine if the following statement is true or false.The first quartile is greater than or equal to 20 hours.

Answer 1

Answer:

Step 1: True

1. Approximately 2000 families are in the sample.

2. False.

3. 31.2 hours.

4. False.

Step-by-step explanation:

The 55th percentile is greater than or equal to 30 hours.

The median is of 31.2 hours, which means that the 50th percentile is of 31.2 hours. The 55th percentile is above the 50th percentile, and thus, the 55th percentile is greater than 31.2 hours, and thus, also greater than 30 hours, and the statement is true.

1: Approximately how many families are in the sample?

Twenty-four of the families in the sample turned on the television for 20 hours or less for the week. The 12th percentile of the data is 20 hours, and thus 24 is 12% of the sample size n. So

$0.12n = 24$

$n = \frac{24}{0.12}$

$n = 2000$

Approximately 2000 families are in the sample.

2: Based on the given information, determine if the following statement is true or false. Approximately 200 families turned on their televisions for less than 35 hours.

The median, that is, the 50th percentile, is of 31.2 hours.

Thus, 35 hours is above the 50th percentile, which means that more than 1000 families(considerably more than 200) will have turned on their TVs for less than 35 hours, and this statement is false.

3: What is the value of the 50th percentile?

The median, which is of 31.2 hours.

4: Based on the given information, determine if the following statement is true or false.The first quartile is greater than or equal to 20 hours.

20 hours is the 12th percentile, which means that the first percentile is less than 20 hours, and this statement is false.