Question

5. A researcher gathers data on how long teenagers spend on individual cell phone calls (in number of minutes). Suppose the research determines that these calls have a mean

10 minutes and standard deviation 7 minutes.
a. Suppose the researcher also claims that the distribution of the call lengths follows a normal distribution. Sketch a graph displaying this distribution. Be sure to add a scale and
to label your horizontal axis.
b. Using your graph, shade the area that represents the probability that a randomly selected call lasts more than 12 minutes. Is this probability closer to 0.50 or to 0.05?
c. After looking at the above mean and standard deviation of the call length data, a second researcher indicates that she does not think that a normal distribution is an appropriate
model for the call length distribution. Which researcher (the first or the second) do you think is correct? Justify your choice.

Answer 1

a) Check graph

b)Closer to 0.5

c)Researcher 1 is right.

Explanation:

a) Please check attached graph.

b) Please check second graph. It is shown that the value is 0.387 which is closer to 0.5.

c) Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. The researcher 1 is right because there are numerous random variables are exist for this event and normal distribution function is the best function that gives less error for this numerous not-known random variables.