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vova2212 [387]
3 years ago
14

Help pleaseeeee?????

Mathematics
1 answer:
BARSIC [14]3 years ago
4 0
H i think is the answer
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3 years ago
The American Community Survey showed that residents of New York City have the longest travel times to get to work compared to re
LiRa [457]

Answer:

The probability it will take a resident of the city between 17.24 and 42.13 minutes to travel to work is 0.3046.

Step-by-step explanation:

The random variable <em>X</em> can be defined as the travel times to get to work.

The expected travel time is, <em>μ</em> = 38.3 minutes.

The distribution of random variable <em>X</em> can be defined as the distribution of time interval between which a person reaches their work place at a constant average rate.

This implies that <em>X</em> follows an Exponential distribution with parameter, \lambda=\frac{1}{\mu}=\frac{1}{38.3}.

The probability density function of <em>X</em> is:

f_{X}(x)=\lambda e^{-\lambda x};\ x\geq 0

Compute the probability it will take a resident of the city between 17.24 and 42.13 minutes to travel to work as follows:

P(17.24\leq X\leq 42.13)=\int\limits^{42.13}_{17.24}{\frac{1}{38.3} e^{-x/38.3}}}\, dx

                                   =\frac{1}{38.3}\times \int\limits^{42.13}_{17.24}{ e^{-x/38.3}}}\, dx

                                   =\frac{1}{38.3}\times| \frac{e^{-x/38.3}}{-1/38.3}}|^{42.13}_{17.24}\\

                                   =-e^{42.13/38.3}+e^{17.34/38.3}\\=-0.3329+0.6375\\=0.3046

Thus, the probability it will take a resident of the city between 17.24 and 42.13 minutes to travel to work is 0.3046.

6 0
3 years ago
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