A normal distribution has a standard deviation equal to 23. What is the mean of this normal distribution if the probability of scoring above x = 181? record to 1 decimal place
Probability must always be one or less. Need more and accurate data.
To find the mean of a normal distribution, we need some additional information. In this case, we know the standard deviation (σ) is equal to 23, but we also need to know the specific value of the random variable (x) for which we want to find the probability.
The formula to calculate the probability of scoring above a certain value in a normal distribution is as follows:
P(X > x) = 1 - P(X ≤ x)
Since we are given the probability P(X > 181), we can rewrite the equation as:
P(X > 181) = 1 - P(X ≤ 181)
To solve this equation, we need to consult a standard normal distribution table or use statistical software. The table provides the cumulative probability (P(X ≤ x)) for different values of x. By subtracting the cumulative probability from 1, we can find P(X > x).
Using the table or statistical software, we find that the cumulative probability corresponding to x = 181 is approximately 0.5726. Subtracting this value from 1, we get:
P(X > 181) = 1 - 0.5726
P(X > 181) ≈ 0.4274
Now, to find the mean of the normal distribution, we need to use the cumulative distribution function (CDF) or the inverse of the cumulative distribution function (CDF^-1). Unfortunately, without more specific information, we cannot determine the mean directly from the given probability.