Question A : In San Francisco, 30% of workers take public transportation daily.
ID: 3209182 • Letter: Q
Question
Question A :
In San Francisco, 30% of workers take public transportation daily. For a sample of 10 workers.
Please compute P(x < 4) and Var [x]
Question B :
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minutes.
Compute the P(x 7) and P(x > 11)
Question C :
A company that produces Headphones has two different plant locations, one located in North Carolina and one in Montana. In North Carolina there are 80 employees and in Montana there are 55 employees. The company wants to test their newest headphones and has decided to give away 30 pairs to a randomly selected group of employees. Compute the following probabilities.
What is the probability that half the headphones go to employees at the Montana plant?
What is the probability that at least 10 employees at the Montana plant receive headphones?
Explanation / Answer
As multiple questions are posted, only the first one will be answered.
A. Number of workers taking public transportation daily follows a binomial distribution with n=10 and p = 0.30
P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
= 5C0*0.300*(1-0.30)5-0 + 5C1*0.301*(1-0.30)5-1 + 5C2*0.302*(1-0.30)5-2 + 5C3*0.303*(1-0.30)5-3
= 0.6496
Var[X} = n*p*(1-p) = 10*0.3*0.7 = 2.1