Respuesta :
Answer:
2614 cars will be driven by females, give or take 28.
Step-by-step explanation:
For each Ford vehicle, there are only two possible outcomes. Either it is driven by a female, or it is not. Cars are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Company determined that the probability of a randomly selected Ford vehicle on the road being driven by a female is 0.71.
This means that [tex]p = 0.71[/tex]
If there are 3,682 Ford vehicles in your town
This means that [tex]n = 3682[/tex]
__________ cars will be driven by females, give or take __________.
The mean and the standard deviation complete this. So
Mean: [tex]E(X) = np = 3682*0.71 = 2614[/tex]
Standard deviation: [tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{3682*0.71*0.29} = 28[/tex]
2614 cars will be driven by females, give or take 28.
