Hello Patricia,
Let X represent the lifetime of a randomly selected CD player. Then, as in the information you provide, X is normally distributed with a mean μ = 2.3 years and a standard deviation σ = .4 years. You want to find the probability that a CD player will break down within 2 years. That is, you want to find P(X ≤ 2). To find this probability, we must convert X to a standard normal random variable (represented as Z) using the equation
Z = (X - μ)/σ
Finding the value of Z corresponding to X = 2, we have
Z = (2 - 2.3)/.4 = -.75
Thus,
P(X ≤ 2) = P(Z ≤ -.75)
P(Z ≤ -.75) is the same as the area under the standard normal curve to the left of Z = -.75. Looking this up in a table of the standard normal distribution (or using a calculator or computer application with the necessary function), we obtain the result
P(X ≤ 2) = P(Z ≤ -.75) = .2266
Hope that helps!
William
