If the crate took 8 seconds to go from traveling at 2 meters per second one way to moving at 2 meters per second in the opposite
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Answer:
d) 300 times for the first game and 30 times for the second
Step-by-step explanation:
We start by noting that the coin is fair and the flip of a coin has a probability of 0.5 of getting heads.
As the coin is flipped more than one time and calculated the proportion, we have to use the <em>sampling distribution of the sampling proportions</em>.
The mean and standard deviation of this sampling distribution is:
We will perform an analyisis for the first game, where we win the game if the proportion is between 45% and 55%.
The probability of getting a proportion within this interval can be calculated as:
referring the z values to the z-score of the standard normal distirbution.
We can calculate this values of z as:
If we take into account the z values, we notice that the interval increases with the number of trials, and so does the probability of getting a value within this interval.
With this information, our chances of winning increase with the number of trials. We prefer for this game the option of 300 games.
For the second game, we win if we get a proportion over 80%.
The probability of winning is:
The z value is calculated as before:
As (p*-p)=0.8-0.5=0.3>0, the value z* increase with the number of trials (N).
If our chances of winnings depend on P(z>z*), they become lower as z* increases.
Then, we can conclude that our chances of winning decrease with the increase of the number of trials.
We prefer the option of 30 trials for this game.
Here we get the statement:
"sec^-1(0.5) is undefined"
And we want to see if this is true or false, so let's use the properties that we know to find that this is false.
Remember that the sec function is defined as:
Then we will have:
Then is really trivial to see that:
Then we can conclude that the function is not undefined at 0.5, so the statement is false.
Below you can see the graph of the given function, and you will see that it is never undefined.
If you want to learn more, you can read:
