Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a standard deviation of 10 hours. What is the probability that a single battery randomly selected from the population will have a life between 70 and 80 hours?
A) 0.2412
B) 0.3830
C) 0.1712
D) 0.5121

Question

Quizplus · Accepted Answer

To find the probability that a single battery will have a life between 70 and 80 hours, we use the properties of the normal distribution. First, we calculate the z-scores for 70 and 80 hours:For 70 hours: $Z = \frac{70 - 75}{10} = -0.5$For 80 hours: $Z = \frac{80 - 75}{10} = 0.5$Using standard normal distribution tables or a calculator, we find the probabilities corresponding to these z-scores:The probability of a z-score being less than 0.5 is approximately 0.6915, and the probability of a z-score being less than -0.5 is approximately 0.3085. The probability of a battery lasting between 70 and 80 hours is the difference between these two probabilities:$0.6915 - 0.3085 = 0.3830$Therefore, the correct answer is 0.3830.

Suppose the Life of a Particular Brand of Calculator Battery