Question

An automobile battery manufacturer claims that its midgrade battery has a mean life of 50 months with a standard deviation of 6. Suppose the distribution of battery lives of this particular brand is approximately normal. On the assumption that the manufacturer’s claim true, find the probability that a randomly selected battery of this type will last less than 48 months.

Answer 1

The probability that a midgrade battery will last less than 48 months, given a normal distribution with a mean of 50 months and a standard deviation of 6 months, is approximately 36.94%.

Step-by-step explanation:

To find the probability that a randomly selected midgrade battery will last less than 48 months, assuming the battery life is normally distributed with a mean of 50 months and a standard deviation of 6 months, we use the standard normal distribution (Z-score).

The Z-score is calculated using the formula Z = (X - μ) / σ, where X is the value for which we want to find the probability, μ is the mean, and σ is the standard deviation. For X = 48 months, μ = 50 months, and σ = 6 months, the Z-score calculation is:

Z = (48 - 50) / 6 = -2 / 6 = -0.3333.

Next, we can look up the Z-score in a standard normal distribution table or use a calculator to find the probability corresponding to Z = -0.3333.

The probability that a battery lasts less than 48 months is about 0.3694 (or 36.94%).