# Statistics 6

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## Current revision as of 02:27, 17 June 2010

**Among U.S. cities with a population of more than 250,000 the mean ,one-way commute to work is 24.3 minutes. The longest one-way travel time is New York City, where the mean time is 38.2 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.0 minutes.**

**(a) What percent of the New York City commutes are for less than 28 minutes? (Round your answers to 2 decimal places.)**

**Solution:** we have, mean = μ = 38.2

S.D. = σ = 7

Sample mean = X = 28

P(x<28) = ?

So z = (X - μ) / σ = (28 - 38.2) / 7 = -1.457 = -1.46

Putting the values in in normal distribution calculator or from the Z table we get

P(x<28) = 0.07254 = 7.25 %

**(b) What percent are between 28 and 33 minutes? (Round your answers to 2 decimal places.)**

**Solution:** P(28<x<33) = P(x<33) – P(x<28)

z1 = (X1 - μ) / σ = (28 - 38.2) / 7 = 1.457 = -1.46

z2 = (X2 - μ) / σ = (33 - 38.2) / 7 = -0.742 = 0.74

Putting the values in in normal distribution calculator or from the Z table we get

P(28<x<33) = P(x<33) – P(x<28) = 15.62 %