Answer:
Sure. Here are the steps on how to find the area P(x>290) when the mean is 304 and the standard deviation is 8:
Convert the mean and standard deviation to z-scores.
The z-score is a way of standardizing a distribution so that it has a mean of 0 and a standard deviation of 1. To calculate the z-score for a given value, we use the following formula:
z = (x - μ) / σ
where:
x is the value we are interested in
μ is the mean of the distribution
σ is the standard deviation of the distribution
In this case, the mean is 304 and the standard deviation is 8, so the z-score for 290 is:
z = (290 - 304) / 8 = -2.00
Find the area under the standard normal curve that corresponds to the z-score.
We can use a z-table to find the area under the standard normal curve that corresponds to a given z-score. The z-table is a table that lists the area under the standard normal curve for different z-scores.
Looking up the z-score of -2.00 in the z-table, we find that the area is 0.0228.
Multiply the area by 100 to get the probability.
The area under the standard normal curve is expressed as a percentage. To get the probability, we need to multiply the area by 100.
In this case, the area is 0.0228, so the probability is 2.28%.
Therefore, the area P(x>290) when the mean is 304 and the standard deviation is 8 is 2.28%.
Explanation: