A game has 15 balls for each of the letters B, I, N, G, and O. The table shows the results of drawing balls 1,250 times.

1 answer:

4 0

Theoretically, each letter should have the same probability of occurring since there are 15 of each. There are 5 letters that can be drawn, so there is a total of 75 balls, and each letter has a probability $\dfrac{15}{75}=\dfrac15$ of being drawn.

This means one would expect a theoretical frequency of $\dfrac{1250}5=250$ , i.e. any given letter should get drawn 250 times, which means the answer is D.

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Find all polar coordinates of point P = (6, 31°).

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as far as I can tell, is just a matter of going around the circle many or infinite times around.

so 6,31° is the first point, the next point will be one-go-around, 6, 31+360 => 6, 391°

then the next will be 6, 391+360 => 6, 751° and so on.

so we can say is (6, 31° ±360°n), n ∈ ℤ.

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The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

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Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$