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Find the Area
P(x>290)
Mean: 304
Standard Deviation: 8

User Joeln
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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:

User Mukiza Andrew
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