Problem 45

Given information

Use the following information to answer the next two exercises: The life of Sunshine CD players is normally distributed with a mean of  years and a standard deviation of    years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts.

Step-by-step explanation

The probability gives the likelihood of a specific event that it will occur.

The value of probability lies between  and  The probability of a random variable say  is usually denoted by .

Therefore, the probability of the random variable assuming any specified value is denoted by .

The probability of the random variable assuming less than or left of any specified value is , and the probability of the random variable assuming more than or right of any specified value is .

The two types of probability distribution are as follows:

Discrete probability distribution: A discrete probability distribution describes the probability of occurrence for each value of a discrete random variable.

Continuous probability distribution: A continuous probability distribution describes the probabilities of the possible values of a continuous random variable. The continuous distribution of a single point is always zero.

It is to prove that,

Consider the right-hand side of the equation

Therefore,  is equal to because in the case of a continuous distribution.