Question

A distribution has u=50 and standard deviation =6. In a graphical representation of the distribution, where would the score X=20 appear? a Just right of the peak of the curve b Just left of the peak of the score c in the left tail of the curve d in the right tail of the curve

Answer 1

In a distribution with a mean of 50 and a standard deviation of 6, the score X=20 would be 5 standard deviations below the mean and would thus appear in the left tail of the graphical representation of the distribution, indicating an extreme value with a low probability.

Step-by-step explanation:

If we have a distribution with a mean (μ) of 50 and a standard deviation (σ) of 6, we would expect most of the values to fall within certain ranges about the mean. As mentioned, about 68 percent of the x values lie within one standard deviation from the mean, which would be between 44 (50 - 6) and 56 (50 + 6) in this case.

Now, the score X=20 is significantly lower than the mean. To find out where this would be placed on a graph, we calculate how many standard deviations away from the mean it is: (20 - 50) / 6 = -30 / 6 = -5. This indicates that X=20 is 5 standard deviations below the mean. In a graph of a normal distribution, a value that is 5 standard deviations away from the mean would fall deep within the left tail of the curve.

Therefore, the score X=20 would appear in the left tail of the curve, far from the peak, indicating a very low probability for a score to be this extreme in a normal distribution.