Question

pre - test
the graph shows the distribution of time (in hours) that teenagers spend playing video games per week.
which statement describes the distribution?
the distribution is approximately normal, with a mean of 14 hours and a standard deviation of 8 hours.
the distribution is approximately normal, with a mean of 14 hours and a standard deviation of 4 hours.
the distribution is approximately normal, with a mean of 4 hours and a standard deviation of 14 hours.
the distribution is uniform, with a mean of 14 hours and a standard deviation of 4 hours.

Explanation:

• Shape: The graph is bell - shaped, which is characteristic of a normal distribution. So, it is not a uniform distribution (eliminates the last option).
• Mean: The peak (center) of the normal distribution is at \(x = 14\) hours. So, the mean \(\mu=14\) hours (eliminates the third option which has a mean of 4 hours).
• Standard Deviation: In a normal distribution, about \(68\%\) of the data lies within \(\mu\pm\sigma\), \(95\%\) within \(\mu\pm2\sigma\), and \(99.7\%\) within \(\mu\pm3\sigma\). If \(\mu = 14\) and \(\sigma=8\), then \(\mu - \sigma=14 - 8=6\) and \(\mu+\sigma=14 + 8 = 22\). If \(\sigma = 4\), then \(\mu-\sigma=14-4 = 10\) and \(\mu+\sigma=14 + 4=18\). Looking at the spread of the normal curve (the width of the bell - curve), a standard deviation of 4 is more appropriate as the curve is narrower (a larger standard deviation would make the curve wider).

Answer:

The distribution is approximately Normal, with a mean of 14 hours and a standard deviation of 4 hours.