SOLUTION: A.Three hundred thirthy five students participated in a field demonstration.Their heights averaged 105 cm with a standard deviation of 5cm. 1.What is the probability that a studen

Question 1180480: A.Three hundred thirthy five students participated in a field demonstration.Their heights averaged 105 cm with a standard deviation of 5cm.
1.What is the probability that a student picked at random has a height greater than 116cm?
2.What is the probability that height of a student picked at random is less than 104cm?
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
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%.

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