Question

The following data represents the weights (in grams) of a random sample of 40 candies:

0.97, 0.88, 0.81, 0.83, 0.83, 0.88, 0.99, 0.85, 0.95, 0.83, 0.84, 0.89, 0.77, 0.88, 0.98, 0.84, 0.71,
0.81, 0.71, 0.82, 0.92, 0.78, 0.77, 0.92, 0.83, 0.91, 0.91, 0.85, 0.81, 0.79, 0.98, 0.84, 0.79, 0.75,
0.84, 0.79, 0.81, 0.88, 0.88, 0.79, 0.71, 0.96, 0.72, 0.74, 0.82, 0.84, 0.89, 0.94, 0.93, 0.82

1. Use the empirical rule to determine the percentage of candies with weights between .71 and .99 grams

Hint x=.85

Answer 1

0.97 0.88 0.81 0.83 0.83 0.88 0.99 0.85 0.95 0.83 0.84 0.89 0.77 0.88 0.98 0.84 0.71 0.81 0.71 0.82 0.92 0.78 0.77 0.92 0.83 0.91 0.91 0.85 0.81 0.79 0.98 0.84 0.79 0.75 0.84 0.79 0.81 0.88 0.88 0.79 0.71 0.96 0.72 0.74 0.82 0.84 0.89 0.94 0.93 0.82

Since we know that

P(0.71<x<.99)=P(0.85-0.14<x<0.85+0.14)

=P(x-2s<x<x+2s) = 95%

From the empirical rule