Suppose that the random variable X is normally distributed with a mean = 1000 and standard deviation = 100. Sketch and find each of the following...

Suppose that the random variable X is normally distributed with a mean μ = 1000 and standard deviation σ = 100. Sketch and find each of the following probabilities.a) P(1000 ≤ x ≤ 1200)b) P(x > 1257)c) P(x < 1035)d) P(857 ≤ x ≤ 1183)e) P(x ≤ 700)f) P(812 ≤ x ≤ 913)g) P(x > 891)h) P(1050 ≤ x ≤ 1250)

Suppose that the random variable X is normally distributed with a mean μ = 1000 andstandard deviation σ = 100. Sketch and find each of the following probabilities.Here,a) P(1000 ≤ x ≤...