the life span of an electric bulb is normally distribution with mean 5500 light hours and standard deviation of 1200 light hours . what is the probability that a randomly selected bulb which lasts more than 6000 light hours?
well, 6000 is 5/12 std above the mean.
Look that up in your Z table.
You can play around with this stuff at
http://davidmlane.com/hyperstat/z_table.html
To find the probability that a randomly selected bulb lasts more than 6000 light hours, we can standardize the distribution using Z-scores and then calculate the corresponding probability from the standard normal distribution.
The Z-score formula is given by:
Z = (X - μ) / σ,
where X is the observed value, μ is the mean, and σ is the standard deviation.
Let's calculate the Z-score for 6000 light hours:
Z = (6000 - 5500) / 1200
Z = 500 / 1200
Z ≈ 0.4167
Now, we need to find the probability associated with this Z-score. We can use a Z-table or a statistical software to determine the area under the standard normal distribution curve to the right of Z = 0.4167.
Using a Z-table, the probability corresponding to Z = 0.4167 is approximately 0.6591.
Therefore, the probability that a randomly selected bulb lasts more than 6000 light hours is approximately 0.6591, or 65.91%.
To find the probability that a randomly selected bulb lasts more than 6000 light hours, we need to use the concept of the standard normal distribution.
Step 1: Standardizing the value
First, we need to standardize the value 6000 using the formula:
z = (x - μ) / σ
where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.
In this case, the mean μ = 5500 and the standard deviation σ = 1200.
Plugging in the values:
z = (6000 - 5500) / 1200
z = 500 / 1200
z = 0.4167 (rounded to 4 decimal places)
Step 2: Finding the probability
Next, we need to find the probability of a value greater than the standardized value of 0.4167 using a standard normal distribution table or a calculator.
Using a standard normal distribution table, we look up the z-score of 0.4167. The table provides the probability associated with the z-score. Let's assume it is p.
The probability of a randomly selected bulb lasting more than 6000 light hours can be found by subtracting the probability associated with the z-score from 1 (since we want the probability of it lasting more than 6000 hours).
Probability = 1 - p
Please note that the exact value of p will depend on the specific table or calculator used, as the values may vary slightly. Make sure to use a reliable source for the standard normal distribution table or calculator.
Once you find the value of p, subtract it from 1 to get the final probability.