Question 1193306
**1. Define Variables**

* Let X be the random variable representing the number of calories burned per hour.
* X follows a normal distribution with:
    * Mean (μ) = 300 calories
    * Standard deviation (σ) = 8 calories

**2. Standardize the Values**

* We'll use the z-score formula: 
    * z = (X - μ) / σ

**A. Less than 294 calories**

* Calculate the z-score for X = 294:
    * z = (294 - 300) / 8 = -0.75

* Find the probability:
    * P(X < 294) = P(Z < -0.75) 
    * Using a standard normal distribution table or a calculator, we find P(Z < -0.75) ≈ 0.2266

* **Therefore, the probability of burning less than 294 calories is approximately 0.2266 (or 22.66%).**

**B. Between 278 and 318 calories**

* Calculate the z-scores for X = 278 and X = 318:
    * z1 = (278 - 300) / 8 = -2.75
    * z2 = (318 - 300) / 8 = 2.25

* Find the probability:
    * P(278 < X < 318) = P(-2.75 < Z < 2.25) 
    * P(-2.75 < Z < 2.25) = P(Z < 2.25) - P(Z < -2.75)

    * Using a standard normal distribution table or a calculator:
        * P(Z < 2.25) ≈ 0.9878
        * P(Z < -2.75) ≈ 0.0030

    * P(-2.75 < Z < 2.25) ≈ 0.9878 - 0.0030 = 0.9848

* **Therefore, the probability of burning between 278 and 318 calories is approximately 0.9848 (or 98.48%).**