Suppose that x is normally distributed with a mean of 10 and a standard deviation of 3. Find P(x ¡Ü 6). Note: Round your answer, if necessary, to two places after the decimal. Please express your answer with two places after the decimal.
the symbol inside P(x ¡Ü 6)
did not come out as you intended, and I suppose it is either ≤ or ≥ ro < or >
anyway, this webpage let's you input your values , and replaces the table or chart you are probably using.
http://davidmlane.com/normal.html
To find P(x ≤ 6), we need to calculate the cumulative probability of the Normal Distribution up to the value of 6.
In order to accomplish this, we can use a standard Normal Distribution table or a statistical calculator with functions related to the Normal Distribution.
Here are the steps to find P(x ≤ 6) using a standard Normal Distribution table:
1. Standardize the value: To use the table, we need to convert the value 6 to a standardized z-score using the formula:
z = (x - mean) / standard deviation
In this case, the mean (μ) is 10 and the standard deviation (σ) is 3. So, substituting the values:
z = (6 - 10) / 3
z = -4 / 3
z = -1.33 (rounded to two decimal places)
2. Look up the z-score in the table: Using the standard Normal Distribution table or a calculator, we can find the cumulative probability corresponding to the z-score of -1.33. This probability represents the area under the curve from negative infinity up to the z-score of -1.33.
When we look up -1.33 in the table, we find that P(Z ≤ -1.33) is approximately 0.0918 (rounded to four decimal places).
3. Interpret the result: The probability P(x ≤ 6) represents the likelihood of the random variable x being less than or equal to 6 when it follows a Normal Distribution with a mean of 10 and a standard deviation of 3.
Therefore, P(x ≤ 6) ≈ 0.0918 (rounded to four decimal places).
Note: This solution assumes that x follows a Normal Distribution.