3. Pearl wants to determine the average
number of goals she scored her first five
field hockey games of the season. She
scored 2 goals in the first game, 3 goals
in the second, and 5 goals in the third.
She can't remember how many goals she
scored in the fourth and fifth games but
she does remember that she scored the
same number of times in each of those
games. The expression
2 + 3 + 5 + x + x
will determine the average number of
goals she scored, where x is the number of
goals she scored in each of the fourth and
fifth games.
If Pearl scored 2 goals in each of the
fourth and fifth games, what was her
average number of goals per game?

Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. here are data on the "penetrability" of the same type of soil at two levels of compression. penetrability is a measure of how much resistance plant roots will meet when they try to grow through the soil. compressed soil 2.85 2.66 3 2.82 2.76 2.81 2.78 3.08 2.94 2.86 3.08 2.82 2.78 2.98 3.00 2.78 2.96 2.90 3.18 3.16 intermediate soil 3.17 3.37 3.1 3.40 3.38 3.14 3.18 3.26 2.96 3.02 3.54 3.36 3.18 3.12 3.86 2.92 3.46 3.44 3.62 4.26 use the data, omitting the high outlier, to give a 95% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil. compute degrees of freedom using the conservative method. interval: to