Question

a set of data has a normal distribution with a mean of 47 and a standard deviation of 8. find the percent of data within the following interval. less than 47 the percent of data within the given interval is \\(\square\\)%. (type an integer or a decimal.)

Explanation:

Step1: Recall Normal Distribution Property

In a normal distribution, the mean ($\mu$) is the center of the symmetric bell - shaped curve. The total area under the normal distribution curve is 1 (or 100% when expressed as a percentage). Since the distribution is symmetric about the mean, the area to the left of the mean (values less than the mean) and the area to the right of the mean (values greater than the mean) are equal.

Step2: Calculate the Percentage

Given that $\mu = 47$, and we want to find the percentage of data less than 47. Since the normal distribution is symmetric about the mean, the proportion of data less than the mean is $\frac{1}{2}$ (or 0.5) of the total data. To convert this proportion to a percentage, we multiply by 100: $0.5\times100 = 50\%$.

Answer:

50