the lengths of movie files that are available for streaming are modeled using the normal distribution shown…

the lengths of movie files that are available for streaming are modeled using the normal distribution shown below. the mean of the distribution is 189.4 min and the standard deviation is 20.1 min. in the figure, v is a number along the axis and is under the highest part of the curve. and, u and w are numbers along the axis that are each the same distance away from v. use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of u, v, and w. percentage of total area shaded: (choose one) time (in min)

the lengths of movie files that are available for streaming are modeled using the normal distribution shown below. the mean of the distribution is 189.4 min and the standard deviation is 20.1 min. in the figure, v is a number along the axis and is under the highest part of the curve. and, u and w are numbers along the axis that are each the same distance away from v. use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of u, v, and w. percentage of total area shaded: (choose one) time (in min)

Answer

Explanation:

Step1: Recall empirical rule

The empirical rule for a normal - distribution states that about 68% of the data lies within 1 standard deviation of the mean, about 95% lies within 2 standard deviations of the mean, and about 99.7% lies within 3 standard deviations of the mean. Since (U) and (W) are equidistant from (V) (the mean), and looking at the spread, they are likely 1 standard - deviation away from the mean. So the percentage of the total area shaded is 68%.

Step2: Find the value of (V)

The mean of the distribution is (V). Given that the mean (\mu = 189.4) min, so (V = 189.4) min.

Step3: Find the value of (U)

(U) is 1 standard deviation below the mean. Using the formula (U=\mu-\sigma), where (\mu = 189.4) min and (\sigma = 20.1) min. So (U=189.4 - 20.1=169.3) min.

Step4: Find the value of (W)

(W) is 1 standard deviation above the mean. Using the formula (W=\mu+\sigma), where (\mu = 189.4) min and (\sigma = 20.1) min. So (W=189.4 + 20.1 = 209.5) min.

Answer:

Percentage of total area shaded: 68% (U = 169.3) min (V = 189.4) min (W = 209.5) min