Question

IN An EXCEL FILE USING EXCEL FUNCTIONS CALCULATIONS 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 exatly three workers take public transportation daily? d. What is the probability that NONE of 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? 1) What is the probability at least two but no more than eight workers take public transportation daily?

Answer 1

a) Random variable is workers that take public transport daily.

Probability of worker that take public transport daily p = 0.30

Sample size, n = 10

b) Binomial distribution will be used.

1. As number of observation is fixed

2. Each observation is fixed.

3. Each observation represents one of two outcomes ("success" or "failure").

c) Probability that exactly 3 workers take public transport daily, P(X=3) =

Using excel:

= BINOMDIST(3,10,0.3,0)

= 0.266828

d) Probability that exactly NONE(0) workers take public transport daily, P(X=0) =

= BINOMDIST(0,10,0.3,0)

= 0.028248

e) Probability that more than 5 workers take public transport daily, P(X>5) = 1 - P(X <=5)

= 1 - BINOMDIST(5,10,0.3,1)

= 0.047349

f) Probability that less than 7 workers take public transport daily, P(X<7) = P(X< = 6)

= BINOMDIST(6,10,0.3,1)

= 0.989408

g) Probability that atleast 2 but no more than 8 workers take public transport daily, P(2 <=X<=8) = P(X<=8) - P(X<2)

= P(X< =8) - P(x<=1)

= BINOMDIST(8,10,0.3,1) - BINOMDIST(1,10,0.3,1)

= 0.850548