Question

A particular brand of car battery claims that it lasts 48 months. From past studies of this battery, the standard deviation is known to be 4.9 months. What is the probability that a randomly selected battery will last between 45 and 50 months?

a) 0.1587
b) 0.3413
c) 0.6826
d) 0.8413

Answer 1

To find the probability that a randomly selected battery will last between 45 and 50 months, calculate the z-scores for 45 months and 50 months using the given mean and standard deviation. Use a standard normal distribution table or calculator to find the probabilities associated with these z-scores and then calculate the probability between these two z-scores.

Step-by-step explanation:

To find the probability that a randomly selected battery will last between 45 and 50 months, we need to calculate the z-scores for 45 months and 50 months using the given mean and standard deviation. The formula for calculating the z-score is:

z = (x - mean) / standard deviation

Using the formula, we get:

z1 = (45 - 48) / 4.9 = -0.61

z2 = (50 - 48) / 4.9 = 0.41

Next, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability of a z-score less than -0.61 is approximately 0.2709, and the probability of a z-score less than 0.41 is approximately 0.6591. To find the probability between these two z-scores, we calculate:

Probability = 0.6591 - 0.2709 = 0.3882

Therefore, the probability that a randomly selected battery will last between 45 and 50 months is approximately 0.3882.