Question

Example 1. Assume that the random variable X follows the Normal distribution with mean 75 and standard deviation 10. Use Python to

(a) Compute P(65 < X < 85) and interpret the findings

(b) Compute P(55 < X < 95) and interpret the findings

(c) Compute P(X > 100) and interpret the findings

Example 2. Assume that the random variable X follows the Normal distribution with mean µ and standard deviation σ. Compute

 (a) P(µ − σ < X < µ + σ)

 (b) P(µ − 2σ < X < µ + 2σ) 

 (c) P(µ − 3σ < X < µ + 3σ) 

(Hint: convert X to standard normal distribution and use Python) 

Example 3. For a standard normal Z, compute P(Z < −2) 

Example 4. For a standard normal Z, find a point a such that P(Z < a) = 0.05