Statistics 6

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(Created page with ''''Among U.S. cities with a population of more than 250,000 the mean ,one-way commute<br> to work is 24.3 minutes. The longest one-way travel time is New York City, where the<br>…')

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 %

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