Given that x is a normal variable with mean μ = 49 and standard deviation σ = 6.7, find the following probabilities. (Round your answers to four decimal places.) (a) P (x ≤ 60) (b) P (x ≥ 50) (c) P (50 ≤ x ≤ 60)

0.9500, 0.4407, 0.3904

Step-by-step explanation:

(a) P (x ≤ 60). We need to find the area under the standard normal curve to the left of x = 60. The appropriate command when using a TI-83 Plus calculator with statistical functions is normcdf (-1000, 60, 49, 6.7). This comes out to 0.9500. P (x ≤ 60) = 0.9500

(b) P (x ≥ 50) would be normcdf (50, 1000,49, 6.7), or 0.4407

(c) P (50 ≤ x ≤ 60) would be normcdf (50,60,49,6.70, or 0.3904