Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities.

1. P[40 ≤ X ≤ 47]; µ = 50 & σ = 15

2. P[X ≥ 2]; µ = 3 & σ = 0.25

3. Find z such that 97.5% of the standard normal curve lies to the left of z.

4. Find z such that 95% of the standard normal curve lies to the right of z.

5. Find the z value such that 98% of the standard normal curve lies between -z and z.

6. Find the z value such that 95% of the standard normal curve lies between -z and z.