Question

the graph shows the distribution of the number of text messages young adults send per day. the distribution is approximately normal, with a mean of 128 messages and a standard deviation of 30 messages. according to the graph, 99.85% of young adults send fewer than what number of text messages? 38 68 188 218 daily text messaging

Explanation:

Step1: Recall the empirical rule for normal distribution

The empirical rule states that for a normal distribution:

• Approximately \(68\%\) of the data lies within \(1\) standard deviation (\(\mu\pm\sigma\)) of the mean.
• Approximately \(95\%\) of the data lies within \(2\) standard deviations (\(\mu\pm2\sigma\)) of the mean.
• Approximately \(99.7\%\) of the data lies within \(3\) standard deviations (\(\mu\pm3\sigma\)) of the mean.

Step2: Calculate the value for \(99.7\%\) (close to \(99.85\%\))

Given \(\mu = 128\) (mean) and \(\sigma=30\) (standard deviation).
We use the formula \(x=\mu + 3\sigma\)
Substitute the values: \(x = 128+3\times30\)

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Answer:

218