1. The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 50 ounces and a standard deviation of 9 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 99.7% of the widget weights lie between and b) What percentage of the widget weights lie between 41 and 77 ounces? % c) What percentage of the widget weights lie below 68 ? % d) Determine how many of the 180 widgets that Acme company manufactured fall within the 68% range? Round to the nearest whole number.

2. The time needed to complete a math examination is bell-shaped with a mean of 90 minutes and a standard deviation of 15 minutes.

a) What percentage of students will complete the exam in 45 minutes or less?

%

b) Assume that the class has 190 students and that the examination period is 120 minutes in length. How many students do you expect will not be able to complete the exam in the allotted time? Round answer to the nearest whole number.

c) A student is classified as extremely "efficient" if the amount of time spent on the exam is the lowest 2.5% for the distribution. What is the upper limit for the time it takes an extremely "efficient" student to finish the exam?

minutes

3. The five number summary of a dataset was found to be:

-4, 1, 6, 13, 22

a) What is the IQR?

b) Find the lower limit (ie: an observation is considered an outlier if it is below this).

c) Find the upper limit (ie, an observation is considered an outlier if it is above this).

d) Do we have any outliers?yes or no?