Question

A sample of 100 batteries was tested to find the length of life, produced the following results: mean is 22 hours and the standard deviation is 6 hours. Assuming the data to be normally distributed, what percentage of batteries are expected to have life for more than 25 hours?

Answer 1

The percentage of batteries expected to last more than 25 hours, given a normal distribution with a mean of 22 hours and a standard deviation of 6 hours, is approximately 30.85%.

Step-by-step explanation:

The student's question concerns the percentage of batteries expected to last more than 25 hours given the normal distribution of battery life with a mean of 22 hours and standard deviation of 6 hours. To find this percentage, one can use the Z-score formula, which is Z = (X - μ) / σ, where X is the value in question (25 hours), μ is the mean (22 hours), and σ is the standard deviation (6 hours). After calculating the Z-score, you can refer to the standard normal distribution table to find the area to the right of the Z-score, which gives the percentage of batteries lasting more than 25 hours.

For example, to calculate this for the given battery data:

• Calculate the Z-score: Z = (25 - 22) / 6 = 0.5
• Look up Z = 0.5 in the standard normal distribution table to find the area to the left of 0.5, which is typically around 0.6915.
• Subtract this value from 1 to find the area to the right: 1 - 0.6915 = 0.3085 or 30.85%

Hence, approximately 30.85% of the batteries are expected to last more than 25 hours.