Questions: Fifty pro-football rookies were rated on a scale of 1 to 5, based on performance at a training camp as well as on past performance. A ranking of 1 indicated a poor prospect whereas a ranking of 5 indicated an excellent prospect. The following frequency distribution was constructed: Rating Frequency ------ 1 4 2 16 3 14 4 18 5 4 a-1. How many of the rookies received a rating of 4 or better? Number of rookies a-2. How many of the rookies received a rating of 2 or worse? Number of rookies b-1. Construct the corresponding relative frequency distribution. (Round your answers to 2 decimal places.) Rating Relative Frequency ------ 1 2 3 4 5

Solution Steps

To solve the given questions, we will follow these steps:

a-1. To find the number of rookies who received a rating of 4 or better, we will sum the frequencies of ratings 4 and 5.

a-2. To find the number of rookies who received a rating of 2 or worse, we will sum the frequencies of ratings 1 and 2.

b-1. To construct the relative frequency distribution, we will divide the frequency of each rating by the total number of rookies and round the result to two decimal places.

The total number of rookies is calculated by summing the frequencies of all ratings: \[ \text{Total rookies} = 4 + 16 + 14 + 18 + 4 = 56 \]

To find the number of rookies with a rating of 4 or better, sum the frequencies of ratings 4 and 5: \[ \text{Rookies with rating 4 or better} = 18 + 4 = 22 \]

To find the number of rookies with a rating of 2 or worse, sum the frequencies of ratings 1 and 2: \[ \text{Rookies with rating 2 or worse} = 4 + 16 = 20 \]

The relative frequency for each rating is calculated by dividing the frequency of each rating by the total number of rookies and rounding to four significant digits: \[ \text{Relative frequency of rating 1} = \frac{4}{56} \approx 0.0714 \] \[ \text{Relative frequency of rating 2} = \frac{16}{56} \approx 0.2857 \] \[ \text{Relative frequency of rating 3} = \frac{14}{56} \approx 0.2500 \] \[ \text{Relative frequency of rating 4} = \frac{18}{56} \approx 0.3214 \] \[ \text{Relative frequency of rating 5} = \frac{4}{56} \approx 0.0714 \]

Final Answer