Question 1190363: Driving to Work Alone: It is reported that 77% of workers aged 16 and over drive to work alone.
Choose 8 workers at random.
Please, find the probability that
a) All drive to work alone
b) More than one-half drive to work alone
c) Exactly 3 drive to work alone
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Part (a)
n = 8 = sample size
p = 0.77 = probability of success (i.e. picking someone who drives alone)
x = number of drivers who are alone
x takes on the integer values from the set {1,2,...,7,8}
For this part, we'll only worry about x = 8 which is involving everyone sampled driving alone.
B(x) = binomial distribution value
B(x) = (nCx)*(p)^x*(1-p)^(n-x)
B(8) = (8C8)*(0.77)^8*(1-0.77)^(8-8)
B(8) = 0.123574
The nCx refers to the nCr combination formula
Answer: Approximately 0.123574
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Part (b)
n = 8 cuts in half to 4
"more than half" means "more than 4"
We'll need to compute each B(x) value for x = 5, 6, 7 and 8.
The steps are similar to the previous part.
You should find that
B(5) = 0.184 427
B(6) = 0.308 715
B(7) = 0.295 293
B(8) = 0.123 574
all of which are approximate.
Those values add up to 0.912 009
Answer: 0.912009 approximately
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Part (c)
Plug in x = 3 to get...
B(x) = (nCx)*(p)^x*(1-p)^(n-x)
B(3) = (8C3)*(0.77)^3*(1-0.77)^(8-3)
B(3) = 0.016 455
Answer: 0.016455
All results are approximate rounded to 6 decimal places.
Round however else you need if your teacher instructs it.
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