Question 1199323
**a. Probability of a Single Car Performing Poorly**

* **Standardize the value:**
    * z = (X - μ) / σ 
    * z = (20 - 25) / 4 = -1.25

* **Find the probability using a standard normal distribution table or calculator:**
    * P(X ≤ 20) = P(Z ≤ -1.25) ≈ 0.1056

* **Therefore, the probability that a single randomly selected car has an mpg of 20 or below is approximately 0.1056 (or 10.56%).**

**b. Probability of All Five Cars Performing Poorly**

* **Assuming independent events:** Since the performance of each car is independent of the others, the probability of all five cars having an mpg of 20 or below is:

    * P(all five cars ≤ 20 mpg) = P(car 1 ≤ 20 mpg) * P(car 2 ≤ 20 mpg) * ... * P(car 5 ≤ 20 mpg) 
    * P(all five cars ≤ 20 mpg) = (0.1056)⁵ ≈ 0.000012

* **Therefore, the probability that all five randomly selected cars have an mpg of 20 or below is approximately 0.000012 (or 0.0012%).**

**c. Conclusion**

The probability of observing five cars with an mpg of 20 or below, assuming the company's claim is true, is extremely low (0.0012%). This suggests that:

* **The company's claim of an average mpg of 25 might be inaccurate.** 
* **There might be a problem with the production process or the specific batch of cars tested.**

**Further Investigation:**

* **Larger Sample Size:** A larger sample size would provide more robust evidence to support or refute the company's claim.
* **Statistical Testing:** A more formal statistical test, such as a hypothesis test, could be conducted to determine the statistical significance of the observed results.

**Disclaimer:** This analysis assumes that the mpg of the cars follows a normal distribution. 

**Note:** This analysis provides a basic framework. A more rigorous analysis would require considering factors like sampling bias, potential measurement errors, and the specific conditions under which the mpg tests were conducted.