How long sporting events last is quite variable. This variability can cause problems for TV broadcasters, since the amount of commercials and commentator blather varies with the length of the event. As an example of this variability, the table below gives the lengths for a random sample of middle-round contests at the 2008 Wimbledon Championships in women’s tennis.

Match                                                 Length (minutes)

Cirstea-Kuznetsova…………………………  73

Srebotnik-Meusburger……………………..   76

De Los Rios-V. Williams………………….    59

Kanepi-Mauresmo…………………………   104

Garbin-Szavay…………………………….   114

Bondarenko-Lisicki……………………….   106

Vaidisova-Bremond………………………     79

Groenefeld-Moore………………………..     74

Govortsova-Sugiyama………………........    142

Zheng-Jankovic…………………………..     129

Perebiynis-Bammer……………………….     95

Bondarenko-V.Williams………………….     56

Coin-Mauresmo…………………………..     84

Petrova-Pennetta…………………………     142

Wozniacki-Jankovic………………………   106

Groenefeld-Safina………………………...    75

(a) Assume that match lengths are normally distributed. Use Theorem 7.5.1 to construct a 95% confidence interval for the standard deviation of match lengths.

(b) Use these same data to construct two one-sided 95% confidence intervals for σ.