Question

In San Francisco, 15% of workers take public transportation daily.

A) In a sample of 20 San Fransisco workers what is the probability that between 9 and 10 workers take public transportation daily?

B) In a sample of 19 San Fransisco workers what is the probability that at most 5 workers take public transportation daily?

C) In a sample of 19 San Fransisco workers what is the probability that at least 14 workers take public transportation daily?

D) In a sample of 15 San Fransisco workers what is the expected number of workers who take public transportation daily?

E) In a sample of 15 San Fransisco workers what is the variance of the number of workers who take public transportation daily?

Answer 1

In San Francisco, 15% of workers take public transportation daily.

A) In a sample of 20 San Fransisco workers what is the probability that between 9 and 10 workers take public transportation daily?

Here, p= Percentage of workers take public transportation daily.= 0.15

       q = 1 - p =1-0.15% = 0.85

      n = number of Sun Fransisco workers = 20.

Here we use binomial distribution to find probability .

P( between 9 to 10) = P(9)+P(10)

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In a sample of 19 San Fransisco workers what is the probability that at most 5 workers take public transportation daily?

Here p= 0.15 and n = 19 .

Ask to find ,P( at most 5 workers take public transportation daily ) = P( X 5 )

So here , P(0) + P( 1) +P(2) + P(3) + P(4) + P(5) .

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C) In a sample of 19 San Fransisco workers what is the probability that at least 14 workers take public transportation daily?

Here , n= 19, p=0.15

Ask to find P( at least 14 workers take public transportation daily ) =P ( X 14 ) .

So we add x value more than 14 , P(14) + P(15) + P(16) + P(17) + P(18) + P(19) .

Here we use excel command as,

P(14) : =BINOMDIST(14,19,0.15,0)   : 1.50618E-08

P(15) : =BINOMDIST(15,19,0.15,0)   : 8.85989E-10

P(16) : =BINOMDIST(16,19,0.15,0)   : 3.90878E-11

P(17) : =BINOMDIST(17,19,0.15,0)   : 1.21727E-12

P(18) : =BINOMDIST(18,19,0.15,0)   : 2.3868E-14

P(19) : =BINOMDIST(19,19,0.15,0)   : 2.21684E-16

                         

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D) In a sample of 15 San Fransisco workers what is the expected number of workers who take public transportation daily?

We use formula of mean for binomial distribution :

The expected number of workers who take public transportation daily :

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E) In a sample of 15 San Fransisco workers what is the variance of the number of workers who take public transportation daily?

The variance of the number of workers who take public transportation daily :

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