Kelso Motor Parts produces a car battery with a useful life that has a normal distribution.Average life is 40,000 miles, with a standard deviation of 1500 miles.What proportion of the batteries will have a useful life between 42,000 and 44,000 miles?
A).157
B).128
C).088
D).072
E).163

Question

Quizplus · Accepted Answer

To find the proportion of batteries with a useful life between 42,000 and 44,000 miles, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For 42,000 miles, Z = (42000 - 40000) / 1500 = 1.33. For 44,000 miles, Z = (44000 - 40000) / 1500 = 2.67. Looking these Z-scores up in a standard normal distribution table gives the probabilities of 0.9082 and 0.9963, respectively. The difference, 0.9963 - 0.9082, gives the proportion of batteries between these two lifespans, which is approximately 0.088 or 8.8%.

Kelso Motor Parts Produces a Car Battery with a Useful