Question: 1. Explain why, for a continuous random variable, P(X = k) = 0 for any number k. 2. Suppose that a certain battery is advertised

1. Explain why, for a continuous random variable, P(X = k) = 0 for any number k.

2. Suppose that a certain battery is advertised to last for 5 years. Suppose further that the actual life time of the battery is approximately normally distributed with a mean of 5.4 years and a standard deviation of 0.3 years. Answer each of the following:

a) Explain how the standard normal curve, Z, relates to computing the probability of a randomly selected battery lasting less than the advertised amount of time.

b) Compute and interpret the probability of a randomly selected battery lasting less than the advertised amount of time.

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