Part (d) Find the probability that his shirt number is from 34 to 66 OR he weighs at least 291 pounds. Enter your answer

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UpStudy AI · Accepted Answer

To determine the probability that his shirt number is between 34 and 66 **OR** he weighs at least 291 pounds, you can use the formula for the probability of the union of two events:

$$ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) $$

Where:
- $$ P(A) $$ is the probability that his shirt number is between 34 and 66.
- $$ P(B) $$ is the probability that he weighs at least 291 pounds.
- $$ P(A \text{ and } B) $$ is the probability that both conditions are met simultaneously.

**Steps to Calculate:**

1. **Find $$ P(A) $$:** Determine the total number of possible shirt numbers and how many fall between 34 and 66.

$$
   P(A) = \frac{\text{Number of shirt numbers from 34 to 66}}{\text{Total number of possible shirt numbers}}
   $$

2. **Find $$ P(B) $$:** Determine the probability of weighing at least 291 pounds based on the weight distribution provided (e.g., normal distribution parameters if applicable).

3. **Find $$ P(A \text{ and } B) $$:** Determine the probability that both the shirt number is between 34 and 66 **and** the weight is at least 291 pounds.

4. **Apply the Union Formula:**

$$
   P(\text{34 to 66 OR } \geq 291 \text{ lbs}) = P(A) + P(B) - P(A \text{ and } B)
   $$

**Example:**

Assume:
- Shirt numbers range from 1 to 100.
- Weights are uniformly distributed between 200 and 400 pounds.
- Independence between shirt number and weight.

Then:
- $$ P(A) = \frac{66 - 34 + 1}{100} = \frac{33}{100} = 0.33 $$
- $$ P(B) = \frac{400 - 291 + 1}{400 - 200 + 1} = \frac{110}{201} \approx 0.547 $$
- $$ P(A \text{ and } B) = P(A) \times P(B) = 0.33 \times 0.547 \approx 0.180 $$

So,

$$
P(\text{34 to 66 OR } \geq 291 \text{ lbs}) = 0.33 + 0.547 - 0.180 = 0.697
$$

**Final Answer:** The probability is approximately **0.697** or **69.7%**.

*Note:* Adjust the calculations based on the actual distribution and range of shirt numbers and weights provided in your specific problem.
The probability is approximately **0.697** or **69.7%**.

Part (d) Find the probability that his shirt number is from 34 to 66 OR he weighs at least 291 pounds. Enter your answer

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