Binomial Distribution: Railway Driver Survey abt strike act.

A railway company employs a large number of drivers. During a dispute over safety procedures, the drivers consider taking strike action.

Early in the dispute, a polling organisation asks a random sample of 20 of the drivers employed by the company whether they are in favour of strike action.

a) If the probability of a driver answering 'yes' is 0.4 and is independent of the answers of the other drivers, find the probability that 10 or more drivers answer 'yes'.

I used a Cumulative Binomial Distribution Function table:

http://courses.wcupa.edu/rbove/eco252/bintabl1.doc

Using table n = 20, I went across to p = 0.4. The probability that 9 or less answer yes is 0.7553, therefore the probability that 10 or more answer yes is 1 - 0.7553 which is 0.2447. Is that correct?

Later in the dispute, the probability of a driver answering 'yes' rises to 0.6.

b) If the polling organisation asks the same question to a random sample of 20 drivers, find the probability that 10 or more drivers answer 'yes'.

Again I used table n = 20 but it does not have p = 0.6. So if the probability that a driver answers 'yes' is 0.6, the probability they answer 'no' is 0.4. The probability that 10 or less answer 'no' (and therefore 10 or more answer yes) is 0.87248. Is the answer just that?

A union meeting is now called and attended by 20 drivers. at the end of the meeting, those drivers in favour of strike action are asked to raise their hands.

c) Give two reasons why the probability distribution you used in part (b) is unlikely to be suitable for determining the probability that 10 or more of these 20 drivers raise their hands.

Sorry, no idea!

If you could check (a) and (b) and help me with (c), I would be very grateful.

Thank you.

Re: Binomial Distribution: Driver Survey

Monkeyseat said:

c) Give two reasons why the probability distribution you used in part (b) is unlikely to be suitable for determining the probability that 10 or more of these 20 drivers raise their hands.

Sorry, no idea!

The assumption of independance does not hold anymore. In other words, my vote would change if I see how majority is voting on the issue. This is more of a human behavior issue.
If you could check (a) and (b) and help me with (c), I would be very grateful.

Thank you.

Click to expand...

Re: Binomial Distribution: Driver Survey

Subhotosh Khan said:

Monkeyseat said:

c) Give two reasons why the probability distribution you used in part (b) is unlikely to be suitable for determining the probability that 10 or more of these 20 drivers raise their hands.

Sorry, no idea!

The assumption of independance does not hold anymore. In other words, my vote would change if I see how majority is voting on the issue. This is more of a human behavior issue.

If you could check (a) and (b) and help me with (c), I would be very grateful.

Thank you.

Click to expand...

Click to expand...

Thanks.

Okay so I have 1 reason:

The trials aren't independent and so the drivers may be influenced by how other people vote, i.e. their friends.

Could another one be that the probability of a driver answering 'yes' at the meeting may have changed since the drivers had been polled?

Re: Binomial Distribution: Driver Survey

The drivers chose to attend the meeting. Self-selection never constitutes randomness. In a public setting, normally one gets polarization - only the people who are pationate about the issue (one way or the other) show up at the meeting. This creates a massive variance when compared to the entire population - not to mention the greater liklihood that the self-selected distribution is bi-modal, where it may not have been before.

Re: Binomial Distribution: Driver Survey

Thanks for the response. So what you are saying is that only people passionate about the cause will show up, and they are likely to either all vote for strike action or all vote against it, depending on the general consensus? I have seen a similar voting behaviour in a few UK referendums. I didn't quite understand the second half of what you said, mainly because I don't think I'm at that level.

Also, like I stated earlier, could another reason be that the probability of a driver answering 'yes' at the meeting may have changed for one reason or another since the drivers had been polled?

Many thanks.

Re: Binomial Distribution: Driver Survey

tkhunny said:

not to mention the greater liklihood that the self-selected distribution is bi-modal, where it may not have been before.

Click to expand...

But Binomial distribution is always bi-modal ...

Re: Binomial Distribution: Driver Survey

That's very funny. If you take your t-distribution on the road, is it t-mobile?

Okay, get back to work.

Re: Binomial Distribution: Driver Survey

tkhunny said:

That's very funny. If you take your t-distribution on the road, is it t-mobile? <<< No it is a Model-T

Okay, get back to work.

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