Question

the graph shows the distribution of the number of text messages young adults send per day. daily text messaging which statement describes the distribution? the distribution is approximately normal, with a mean of 128 messages and a standard deviation of 98 messages. the distribution is approximately normal, with a mean of 128 messages and a standard deviation of 30 messages. the distribution is approximately normal, with a mean of 30 messages and a standard deviation of 128 messages. the distribution is uniform, with a mean of 128 messages and a standard deviation of 30 messages.

Explanation:

Step1: Analyze the shape of the distribution

The graph is bell - shaped, so it is approximately Normal.

Step2: Determine the mean

The peak of the Normal distribution (which is the mean for a symmetric Normal distribution) is at \(x = 128\).

Step3: Estimate the standard deviation

Using the empirical rule for a Normal distribution (\(68 - 95 - 99.7\) rule). The distance from the mean (\(\mu=128\)) to the inflection point (where the curve changes from concave down to concave up). The inflection point is at \(x = 98\) (since \(128-30 = 98\)) and \(x=158\) (\(128 + 30=158\)). So the standard deviation \(\sigma\approx30\)

Answer:

The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.