Fluorescent lighbulbs have lifetimes that are normally distributed with a mean of 5.8 years and a standard deviation of 1.1 years. The figure below shows the distribution of lifetimes of fluorescent lightbulbs. Calculate the shaded area under the curve.
Fluorescent lighbulbs have lifetimes that are normally distributed with a mean of 5.8 years and a standard deviation of 1.1 years. The figure below shows the distribution of lifetimes of fluorescent lightbulbs. Calculate the shaded area under the curve.
Fluorescent lighbulbs have lifetimes that are normally distributed with a mean of 5.8 years and a standard deviation of 1.1 years. The figure below shows the distribution of lifetimes of fluorescent lightbulbs. Calculate the shaded area under the curve.
Fluorescent lighbulbs have lifetimes that are normally distributed with a mean of 5.8 years and a standard deviation of 1.1 years. The figure below shows the distribution of lifetimes of fluorescent lightbulbs. Calculate the shaded area under the curve.
Transcribed Image Text:The image displays a bell-shaped curve representing a normal distribution of the lifetimes of fluorescent lightbulbs. The x-axis is labeled with two key points: 3.6 and 6.9, which likely represent the number of years or another unit of time.
The shaded region under the curve between these two points highlights the range where most lightbulbs’ lifetimes fall. This shaded area indicates the portion of the lightbulbs that have lifetimes between 3.6 and 6.9 units. The bell shape of the curve suggests that lifetimes are distributed normally, with most lightbulbs having a lifetime near the average value (the peak of the curve), and fewer lightbulbs having lifetimes at the extremes.
The label at the bottom, "Lifetimes of Fluorescent Lightbulbs," provides context for the graph, indicating that the data pertains to how long these lightbulbs last before they fail or burn out. The graph provides a visual representation that helps in understanding the variability and distribution of the product lifespan.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
