Question

In 2016, quarterback Matt Ryan won the NFL's most valuable player award. The two-way table summarizes the association between distance of pass attempt and outcome of pass attempt for Matt Ryan during the 2016 season. Suppose we select one pass attempt at random. Give each answer as a decimal rounded to the thousandths place. Two-Way Table Outcome of pass attempt Complete Incomplete Total Distance of pass attempt (yards) C 10 or less 11-20 21-30 31 or more 281 67 17 8 86 48 16 367 115 33 11 19 Total 373 161 534 7 a.) What is the probability that the pass attempt was at most 10 yards? b.) What is the probability that the pass attempt was more than 10 yards? c.) What is the probability that the pass attempt was at most 10 yards and complete? d.) What is the probability that the pass attempt was at most 10 yards or complete?​

Answer 1

The questions involve calculating probabilities from a two-way table containing NFL quarterback Matt Ryan's pass attempt data. The answers to these questions will be calculated using the total number of pass attempts and the information provided in the table.

Step-by-step explanation:

The questions posed deal with calculating probabilities based on data from a two-way table summarizing the pass attempts of NFL quarterback Matt Ryan during the 2016 season.

To answer these questions, we will use the data provided in the two-way table to calculate:

1. The probability that the pass attempt was at most 10 yards.
2. The probability that the pass attempt was more than 10 yards.
3. The probability that the pass attempt was at most 10 yards and complete.
4. The probability that the pass attempt was at most 10 yards or complete.

We will first determine the total number of pass attempts and then calculate the relevant probabilities using that total.

Answer 2

a) To find the probability that the pass attempt was at most 10 yards, we need to sum up the values in the "Complete" and "Incomplete" categories for the "10 or less" distance.

Complete: 281

Incomplete: 86

Total: 281 + 86 = 367

Probability = (281 + 86) / 534 ≈ 0.897

b) To find the probability that the pass attempt was more than 10 yards, we need to sum up the values in the "Complete" and "Incomplete" categories for distances greater than "10 or less".

Complete: 67 + 17 + 8 = 92

Incomplete: 48 + 16 + 33 + 11 + 19 = 127

Total: 92 + 127 = 219

Probability = (92 + 127) / 534 ≈ 0.410

c) To find the probability that the pass attempt was at most 10 yards and complete, we look at the value in the "Complete" category for the "10 or less" distance.

Complete: 281

Probability = 281 / 534 ≈ 0.526

d) To find the probability that the pass attempt was at most 10 yards or complete, we need to sum up the values in the "Complete" category for all distances and the values in the "10 or less" distance for both "Complete" and "Incomplete".

Complete: 281 + 67 + 17 + 8 = 373

Incomplete: 86

Total: 373 + 86 = 459

Probability = (373 + 86) / 534 ≈ 0.859