Question

what is a normal distribution? early statisticians noticed the same shape coming up over and over again in different distributions - so they named it the normal distribution. normal distributions have the following features: - symmetric bell shape - mean and median are equal; both located at the center of the distribution - 68% of the data falls within 1 standard deviation of the mean - 95% of the data falls within 2 standard deviations of the mean - 99.7% of the data falls within 3 standard deviations of the mean want to learn more about what normal distributions are? check out this video. drawing a normal distribution example the trunk diameter of a certain variety of pine tree is normally distributed with a mean of μ = 150cm and a standard deviation of σ = 30cm. sketch a normal curve that describes this distribution. solution: step 1: sketch a normal curve. step 2: the mean of 150cm goes in the middle. step 3: each standard deviation is a distance of 30cm. the heights of the same variety of pine tree are also normally distributed. the mean height is μ = 33m and the standard deviation is σ = 3m. which normal distribution below best summarizes the data?

Explanation:

Answer:

A normal distribution is a symmetric - bell - shaped distribution where the mean and median are equal and located at the center of the distribution. Approximately 68% of the data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. For the pine - tree height data with mean \(\mu = 33m\) and standard deviation \(\sigma=3m\), the correct normal distribution graph is the one with the mean at 33, and tick - marks at intervals of 3 (e.g., 30, 36, etc.). Without seeing the exact options clearly labeled, we know the center of the correct curve should be at 33 and the spread should be in increments of 3. The discipline is Mathematics, sub - field is Statistics.