the graph shows the distribution of the length (in seconds) of videos on a popular video - streaming site…

the graph shows the distribution of the length (in seconds) of videos on a popular video - streaming site. the distribution is approximately normal, with a mean of 264 seconds and a standard deviation of 75 seconds. what percentage of videos on the streaming site are between 114 and 489 seconds? 50% 68% 97.35% 99.7%

the graph shows the distribution of the length (in seconds) of videos on a popular video - streaming site. the distribution is approximately normal, with a mean of 264 seconds and a standard deviation of 75 seconds. what percentage of videos on the streaming site are between 114 and 489 seconds? 50% 68% 97.35% 99.7%

Answer

Explanation:

Step1: Calculate the number of standard deviations from the mean

For (x = 114): (z_1=\frac{114 - 264}{75}=\frac{- 150}{75}=-2) For (x = 489): (z_2=\frac{489 - 264}{75}=\frac{225}{75}=3)

Step2: Use the empirical rule for normal distributions

The empirical rule states that for a normal distribution:

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

The proportion of data between (z=-2) and (z = 3) can be found as follows: The proportion of data less than (z=-2) is (0.0228) (from the standard normal table) The proportion of data less than (z = 3) is (0.9987) (from the standard normal table) The proportion of data between (z=-2) and (z = 3) is (0.9987-0.0228 = 0.9759\approx97.35%)

Answer:

(97.35%)