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 16 randomly sampled batteries from the population will have a sample mean life of between 70 and 80 hours?
A) 0.9444
B) 0.5121
C) 0.7124
D) 0.1512

Question

Quizplus · Accepted Answer

To find the probability that the sample mean life of 16 batteries is between 70 and 80 hours, we use the formula for the standard error of the mean: $SE = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. Here, $\sigma = 10$ and $n = 16$, so $SE = \frac{10}{\sqrt{16}} = \frac{10}{4} = 2.5$. Next, we calculate the Z-scores for 70 and 80 hours: $Z_{70} = \frac{70 - 75}{2.5} = -2$ and $Z_{80} = \frac{80 - 75}{2.5} = 2$. Looking up these Z-scores in a standard normal distribution table or using a calculator, we find the probabilities corresponding to Z = -2 and Z = 2, and the area between these Z-scores represents the probability we're interested in, which is approximately 0.9544. However, due to rounding or a typo in the options, the closest provided option is A) 0.9444.

Suppose the Life of a Particular Brand of Calculator Battery