Question: 1. 5.20 A large table is marked with parallel and equidistant lines a distance D apart. A needle of length L( D) is tossed in

1. 5.20 A large table is marked with parallel and equidistant lines a distance D apart. A needle of length L(≤ D) is tossed in the air and falls at random onto the table.

The eighteenth century French scientist Georges-Louis Buffon proved that the probability of the needle falling across one of the lines is 2L

πD

. The Italian math ematician M. Lazzarini carried out an actual experiment in 1901, where the ratio L/D was taken equal to 5/6. He made 3,408 needle tosses and observed that 1,808 of them intersected one of the lines. This resulted in a remarkably accurate estimate of 3.14159292 for π = 3.14159265... (an error of about 2.7 × 10−7).

Do you believe that Lazzarini performed the experiment in a statistically sound way?

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