If the variance of a light bulb is 400 and the mean lifetime of a light bulb is 600 hours. find the probablity of a light bulb lasting at most 622 hours

so SD = ?400 = 20

mean = 600

use
http://davidmlane.com/normal.html
and plug in your values

To find the probability of a light bulb lasting at most 622 hours, we first need to calculate the standard deviation of the light bulb lifetime distribution. The standard deviation is the square root of the variance.

Given that the variance of the light bulb is 400, we have:

Standard Deviation = √400 = 20

Next, we can use the concept of the z-score to calculate the probability. The z-score represents the number of standard deviations a value is away from the mean.

To find the z-score for 622 hours, we use the formula:

z = (x - μ) / σ

Where:
x is the value we want to find the probability for (in this case, 622 hours),
μ is the mean lifetime of the light bulb (600 hours), and
σ is the standard deviation (20 hours).

Plugging in the values, we get:

z = (622 - 600) / 20 = 22 / 20 = 1.1

Now, we can look up the probability associated with a z-score of 1.1 in the standard normal distribution table or use a calculator to find the cumulative probability.

Using a calculator or table, we find that the cumulative probability for a z-score of 1.1 is approximately 0.8643.

Therefore, the probability of a light bulb lasting at most 622 hours is approximately 0.8643, or 86.43%.

To find the probability of a light bulb lasting at most 622 hours, we need to use the concept of the normal distribution.

The normal distribution is a continuous probability distribution that is symmetrical, bell-shaped, and characterized by its mean and variance. In this case, the mean lifetime of a light bulb is given as 600 hours, and the variance is given as 400.

To find the probability, we need to standardize the given time value (622 hours) using the Z-score formula:

Z = (X - μ) / σ

Where:
Z = Standardized score
X = Value to be standardized (622 hours)
μ = Mean (600 hours)
σ = Standard deviation (square root of variance)

First, we need to find the standard deviation (σ) by taking the square root of the variance:

σ = √400 = 20

Now, substitute the values into the Z-score formula:

Z = (622 - 600) / 20
Z = 22 / 20
Z = 1.1

We can now use a standard normal distribution table or a statistical calculator to find the probability associated with the Z-score of 1.1. The probability will represent the area under the curve to the left of the Z-score.

Using a standard normal distribution table, the probability of a Z-score of 1.1 (or less) is approximately 0.8643.

Therefore, the probability of a light bulb lasting at most 622 hours is approximately 0.8643, or 86.43%.