math with business applications

Question

A brisk walk at 4 miles per hour burns an average of 300 calories per hour. If the standard deviation of the distribution is 8 hours, find the percentage of people who walk at 4 miles per hour for 1 hour that will burn off between 285 and 320 calories

Answer 1

Assuming you mean that the standard deviation is 8 calories per hour, this question is asking how much of probability curve is located between 285 and 320 calories per hour.

Step 1: Calculate z-scores (for normal distribution).

z = (x - μ) / σ

z₁ = (320 - 300) / 8 = 20 / 8 = 2.5

z₂ = (285 - 300) / 8 = 15 / 8 = 1.875

Step 2: Identify the appropriate portion of the curve.

The portion between z₁ and z₂.

Step 3: Evaluate the probability at each z value. (You can use a z-score table or an online calculator, such as https://www.calculator.net/z-score-calculator.html)

P(z <= 2.5) = 99.379%

P(z <= -1.875) = 3.0396%

Ans: P(z <= 2.5) - P(z <= -1.875) = 99.379% - 3.0396%

96.3394%