Question 1180480
Here's how to solve this problem:

**1. Calculate the z-scores:**

A z-score tells you how many standard deviations a particular value is from the mean.  The formula is:

z = (x - μ) / σ

Where:

*   x = the value you're interested in
*   μ = the mean
*   σ = the standard deviation

*   **For x = 116 cm:**
    z = (116 - 105) / 5
    z = 11 / 5
    z = 2.2

*   **For x = 104 cm:**
    z = (104 - 105) / 5
    z = -1 / 5
    z = -0.2

**2. Find the probabilities using a z-table or calculator:**

A z-table (or a calculator with statistical functions) gives you the probability of a value being *less than* a given z-score.

*   **P(height > 116 cm):**  We want the probability of a height *greater* than 116 cm, so we need to find the area to the *right* of z = 2.2.
    P(z > 2.2) = 1 - P(z < 2.2)
    Look up P(z < 2.2) in the z-table. It's approximately 0.9861.
    P(z > 2.2) = 1 - 0.9861 = 0.0139

*   **P(height < 104 cm):** We want the probability of a height *less* than 104 cm, so we need the area to the *left* of z = -0.2.
    P(z < -0.2)
    Look up P(z < -0.2) in the z-table. It's approximately 0.4207.

**Answers:**

1.  The probability that a randomly picked student has a height greater than 116 cm is approximately 0.0139 or 1.39%.

2.  The probability that a randomly picked student has a height less than 104 cm is approximately 0.4207 or 42.07%.