Question

According to a survey, 15% of city workers take the bus to work. Donatella randomly surveys 10 workers. What is the probability that exactly 6 workers take the bus to work? Round the answer to the nearest thousandth.
0.001

0.002

0.128

0.900

Answer 1

Answer: 0.001

Step-by-step explanation:

Binomial probability formula :

$P(x)=^nC_xp^x(1-p)^{n-x}$, where P(x) is the probability of exactly x successes in n trials.

Given : The probability of city workers take the bus to work =15%=0.15

The sample size :n= 10

Now, the probability that exactly 6 put of 10 workers take the bus to work :-

$P(6)=^{10}C_6(0.15)^{6}(1-0.15)^{10-6}\\\\=\dfrac{10!}{6!(10-6)!}(0.15)^6(0.85)^4\\\\=0.0012486552627\approx0.001$

Therefore , the probability that exactly 6 workers take the bus to work = 0.001

Answer 2

Answer:0.001

x=the number of workers taking the bus to work

p= probability of success =(15/100) = 0.15

q= probability of failure =1- p = 0.85

P(X=6) = 10C6(0.15)^6(0.85)^4

            = 0.001