The Normal distribution with mean μ
μ = 6.8 and standard deviation σ
σ = 1.6 is a good description of the Iowa Test vocabulary scores of seventh grade students in Gary, Indiana. This is a continuous probability model for the score of a randomly chosen student. Figure 3.1 (p. 68) pictures the density curve. Call the score of a randomly chosen student X for short.
Note: If necessary, use < = to represent ≤ and > = to represent ≥.
(a) Write the event "the student chosen has a score of 5.2 or lower" in terms of X.
(b) Find the probability of an event which represents "the student chosen has a score of 5.2 or lower".