Question 1191361
Here's how to solve this problem:

**a) Percent living less than 60 years:**

1. **Calculate the z-score:**
   z = (x - μ) / σ
   z = (60 - 73) / 6
   z = -2.17

2. **Find the probability:** Use a z-table or calculator to find the area to the *left* of z = -2.17. This gives the probability of living less than 60 years. P(z < -2.17) ≈ 0.015 or 1.5%

**b) Proportion living between 85 and 90 years:**

1. **Calculate the z-scores:**
   z₁ = (85 - 73) / 6 = 2
   z₂ = (90 - 73) / 6 = 2.83

2. **Find the probabilities:** Use a z-table or calculator.
   P(z < 2) ≈ 0.9772
   P(z < 2.83) ≈ 0.9977

3. **Find the proportion between the two ages:**
   P(2 < z < 2.83) = P(z < 2.83) - P(z < 2) = 0.9977 - 0.9772 ≈ 0.0205

**c) 30th percentile:**

1. **Find the z-score:** The 30th percentile corresponds to a cumulative probability of 0.30. Look up the z-score closest to 0.30 in the z-table; the z-score is approximately -0.52.

2. **Use the z-score formula:**
   x = μ + zσ
   x = 73 + (-0.52 * 6)
   x ≈ 69.88 years

**d) 97th percentile:**

1. **Find the z-score:**  The 97th percentile corresponds to a cumulative probability of 0.97. The z-score is approximately 1.88.

2. **Use the z-score formula:**
   x = μ + zσ
   x = 73 + (1.88 * 6)
   x ≈ 84.28 years

**e) Percent making it past 75:**

1. **Calculate the z-score:**
   z = (75 - 73) / 6
   z = 0.33

2. **Find the probability:** Use a z-table or calculator to find the area to the *right* of z = 0.33. This is 1 - P(z < 0.33). P(z < 0.33) ≈ 0.6293. So, 1 - 0.6293 ≈ 0.3707 or 37.07%