23. Movie lengths IT.' Exercise 21 looked at the running times of movies released in 2005. The standard deviation
of these running times is 19.6 minutes, and the quartiles
are Qi 97 minutes and Q; = 119 minutes.
a) Write a sentence or two describing the spread in
running times based on
i) the quartiles.
ii) the standard deviation.
b) Do you have any concerns about using either of these
descriptions of spread? Explain.

Identify the converse of the following conditional: if a point is in the first quadrant, then its coordinates are positive. if the coordinates of a point are not positive, then the point is not in the first quadrant. if the coordinates of a point are positive, then the point is in the first quadrant. if a point is in the first quadrant, then its coordinates are positive. if a point is not in the first quadrant, then the coordinates of the point are not positive.

Acomposition of transformations maps δxyz to δx"y"z". the first transformation for this composition is , and the second transformation is a 90° rotation about point x'.

Astudy was interested in determining if eating milk chocolate lowered someone's cholesterol levels. ten people's cholesterol was measured. then, each of these individuals were told to eat 100g of milk chocolate every day and to eat as they normally did. after two weeks, their cholesterol levels were measured again. is there evidence to support that their cholesterol levels went down? how should we write the alternative hypothesis? (mud = the population mean difference= before - after)a. ha: mud = 0b. ha: mud > 0c. ha: mud < 0d. ha: mud does not equal 0