Question

a box of led light bulbs was tested to see how long the light bulbs last. the standard deviation of the light bulb lifetime data was five years. which of the following is the best interpretation of this value? fifty percent of the light bulb lifetime data is below five years. the difference between the longest and shortest light bulb lifetime was five years. the lifetime of the light bulbs typically varies by about five years from the mean. the middle half of the light bulb lifetime data has a range that is five years wide.

Explanation:

Step1: Recall standard - deviation concept

Standard deviation measures the amount of variation or dispersion of a set of values. It represents how far, on average, each data point is from the mean.

Step2: Analyze each option

• Option 1: Fifty percent of the data being below a value refers to the median, not standard - deviation.
• Option 2: The difference between the longest and shortest values is the range, not standard - deviation.
• Option 3: This is the correct interpretation of standard deviation. It indicates that the lifetime of the light bulbs typically varies by about five years from the mean.
• Option 4: The range of the middle half of the data is the inter - quartile range, not standard - deviation.

Answer:

The lifetime of the light bulbs typically varies by about five years from the mean.