A distribution of values is normal with a mean of 61.9 and a standard deviation of 59.3. Find the probability that a randomly selected value is less than 162.7. Shade: Left of a value Click and drag the arrows to adjust the values. 3. 4 -3 -2 T -1 -4 -1.5
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Problem Statement:**
A distribution of values is normal with a mean of 61.9 and a standard deviation of 59.3.
Find the probability that a randomly selected value is less than 162.7.
**Instructions:**
Shade: Left of a value. Click and drag the arrows to adjust the values.
**Diagram Explanation:**
The diagram shows a standard normal distribution curve. The x-axis is marked with standard deviations from -4 to 4. A portion of the curve to the left of the value -1.5 is shaded in blue, indicating the area for which the probability needs to be calculated.
**Equation:**
\[ P(x < 162.7) = P(z < \_\_\_\_ ) = \_\_\_\_ \]
**Answer Submission:**
Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
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Mean = 61.9
Standard deviation = 59.3
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