Question

In San Francisco, 30% of workers take public transportation daily. In a sample of 10 workers,

a.Clearly state what the random variable in this problem is?

b.What is an appropriate distribution to be used for this problem and why?

c.What is the probability that exactly three workers take public transportation daily?

d.What is the probability that NONE of the workers take public transportation daily?

e.What is the probability that more than five workers take public transportation daily?

f.What is the probability that less than seven workers take public transportation daily?

g.What is the probability at least two but no more than eight workers take public transportation daily?

Answer 1

Part a)

Let X :- Is the random variable denote the number of workers takes public transport daily.

Part b)

X ~ B ( n = 10 , P = 0.3 )

Since we have n independent random variable and % of success is also given, hence we use Binomial distribution.

Part c)

Part d)

Part e)

P ( X > 5 ) = 0.0473

Part f)

P ( X < 7 ) = 1 - P ( X >= 7 ) = 1 - 0.0105 = 09895

Part g)

P ( 2 <= X <= 8 ) = 0.8505