Runzheimer International publishes data on overseas business travel costs. They

Question

Runzheimer International publishes data on overseas business travel costs. They report that the average per diem total for a business traveller in Paris, France, is $349. Suppose the shape of the distribution of the per diem costs of a business traveller to Paris is unknown, but that 54% of the per diem figures are between $318 and $380. What is the value of the standard deviation? The average per diem total for a business traveller in Moscow is $415. If the shape of the distribution of per diem costs of a business traveller in Moscow is unknown and if 83% of the per diem costs in Moscow lie between $370 and $460, what is the standard deviation?

Explanation / Answer

As the distribution of the per diem costs of a business traveller to Paris is unknown, we will use Chebyshev's theorem to find out the standard deviation .

average per diem total for a business traveller in Paris, France = $349

So +- k , lie at the between (1 - 1/k2 ) proportion of te value.

so 1- 1/k2 = 0.54

1/k2 = 0.46

k2 = 2.1739

k = 1.4744

so Mean - lower value = k

349 - 318 = 1.4744 *

= 31/ 1.4744 = $21

average per diem total for a business traveller in Moscow, Russia = $415

So +- k , lie at the between (1 - 1/k2 ) proportion of te value.

so 1- 1/k2 = 0.83

1/k2 = 0.17

k2 = 5.88235

k = 2.4255

so Mean - lower value = k

415 - 370 = 2.4255 *

= 45/2.4255 = $18.55

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