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) |
|
d) Probability that exactly NONE(0) workers take public transport daily, P(X=0) =
= BINOMDIST(0,10,0.3,0) |
|
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) |
|
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 |
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eBook Exercise 5.29 (Algorithmic)) In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005) a. In a sample of 6 workers, what is the probability that exactly three workers take public transportation daily (to 4 decimals including interim calculations)? b. In a sample of 6 workers, what is the probability that at least three workers take public transportation dally (to 4 decimals including interim calculations)?
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For this problem, you must use Excel to perform the
necessary calculations. Below are the formulas and equations you
will need to use.
If it is appropriate to use the binomial distribution, use the
formula =binom.dist(number_s,trials,probability,cumulative) to
calculate the probability. In this formula, number_s is the number
of successful trials, trials is the total number of trials,
probability is the probability for a single trial expressed as a
decimal, and cumulative should be set as false. This will report
the...