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3 years ago

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Mathematics

1 answer:

Liula [17]3 years ago

6 0

Answer:

The approximate probability of winning 4 games in a row is 0.012

Step-by-step explanation:

From the question, the probability of winning the shell games if you randomly pick is 1 in 3, that is,

P(Win) = 1/3

Now, the probability of winning 4 games in a row will be

P (winning 4 games in a row) = P(winning 1st game) × P(winning 2nd game) × P(winning 3rd game) × P(winning 4th game)

P (winning 4 games in a row) = (1/3) × (1/3) × (1/3) × (1/3)

P (winning 4 games in a row) = 1/81 or 0.012

Hence, the approximate probability of winning 4 games in a row is 0.012

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jolli1 [7]

Answer:

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

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".

$\bar X=28$ represent the sample mean

$\mu$ population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

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: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.064$

Now we have everything in order to replace into formula (1):

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

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