Question 1200129
**a) Estimate the Standard Deviation**

* **Use the "rule of thumb":** 
   Standard Deviation ≈ (High Value - Low Value) / 4 
   Standard Deviation ≈ (72 beats/min - 14 beats/min) / 4 
   Standard Deviation ≈ 58 beats/min / 4 
   Standard Deviation ≈ 14.5 beats/min

**b) Probability of Heart Rate Less Than 25 bpm**

* **Standardize the value:**
   z = (X - μ) / σ = (25 - 43) / 14.5 ≈ -1.24

* **Find the probability using a z-table:**
   P(X < 25) = P(Z < -1.24) ≈ 0.1075

**c) Probability of Heart Rate Greater Than 60 bpm**

* **Standardize the value:**
   z = (X - μ) / σ = (60 - 43) / 14.5 ≈ 1.17

* **Find the probability using a z-table:**
   P(X > 60) = P(Z > 1.17) ≈ 1 - P(Z < 1.17) ≈ 1 - 0.8790 ≈ 0.1210

**d) Probability of Heart Rate Between 25 and 60 bpm**

* **Find the z-scores:**
    * z1 = (25 - 43) / 14.5 ≈ -1.24 
    * z2 = (60 - 43) / 14.5 ≈ 1.17

* **Find the probability using a z-table:**
   P(25 < X < 60) = P(-1.24 < Z < 1.17) = P(Z < 1.17) - P(Z < -1.24) ≈ 0.8790 - 0.1075 ≈ 0.7715

**e) Heart Rate Corresponding to Upper 13%**

* **Find the z-score for the upper 13%:**
    * Look up the z-score corresponding to the area to the left of 1 - 0.13 = 0.87 in a z-table. 
    * z ≈ 1.13

* **Calculate the heart rate:**
    * X = μ + (z * σ) = 43 + (1.13 * 14.5) ≈ 61.4 

* **Round to the nearest whole number:** 
    * Heart Rate ≈ 61 beats/min

**Summary:**

* (a) Estimated Standard Deviation: 14.5 beats/min
* (b) Probability of Heart Rate < 25 bpm: 0.1075
* (c) Probability of Heart Rate > 60 bpm: 0.1210
* (d) Probability of Heart Rate between 25 and 60 bpm: 0.7715
* (e) Heart Rate for Upper 13%: 61 beats/min