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zvonat [6]
4 years ago
9

Trains on the Glasgow Subway depart every 4 minutes, and a complete circuit takes 24 minutes. Ewan sets off at 8.30 am on a trai

n round in one direction at the same time as another train leaves in the opposite direction. How many trains will he pass on a complete circuit back to his starting station? Do not count trains at the start or end station.
Mathematics
1 answer:
Stolb23 [73]4 years ago
7 0
Trains depart after every 4 minutes.
Total time train takes to complete a circuit= 24 minutes
Evan sets off at 8:30 am, so  he will be back at 8:54 am.
So time of trains coming in opposite direction:
8: 34 am
8:38 am
8:42 am
8:46 am
and 8:50 am
5 trains coming in opposite directions.
Now the trains started at 8:06 am from the stations are:
8:06 am
8:10 am
8:14 am
8:18 am
8:22 am
and 8:26 am.
So there are 6 trains started the circuit at 8:06 am.

Now total number of trains=6+5=11 trains

Answer: 11 trains will pass on complete circuit.

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PilotLPTM [1.2K]

Answer:

e. 0.0072

Step-by-step explanation:

We are given that a bottling company uses a filling machine to fill plastic bottles with cola. And the contents vary according to a Normal distribution with Mean, μ = 298 ml and Standard deviation, σ = 3 ml .

 Let    Z = \frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)  where, Xbar = mean contents of six randomly

                                                                     selected bottles

                                                          n = sample size i.e. 6    

So, Probability that the mean contents of six randomly selected bottles is less than 295 ml is given by, P(Xbar < 295)

 P(Xbar < 295) = P( \frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } } < \frac{295 - 298}{\frac{3}{\sqrt{6} } } ) = P(Z < -2.45) = P(Z > 2.45)

Now, using z% score table we find that P(Z > 2.45) = 0.00715 ≈ 0.0072 .

Therefore, option e is correct .

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Answer:

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A. <em>One has 90​% confidence that the sample proportion is equal to the population proportion. </em>

Confidence interval gives an interval estimate, not an equality

B. <em>There is a 90​% chance that the true value of the population proportion will fall between the lower bound and the upper bound. </em>

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Also true but <em>One has 90​% confidence is not good interpretation. </em>

<em>D</em><em>. 90​% of sample proportions will fall between the lower bound and the upper bound.</em>

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The probability that it will rain tomorrow is 0.65
tatiyna
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