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Featured 9 months ago

Approximately, arithmetic mean equals to

First, the theory behind the method.

If a random variable *mean*, **by definition**, equals to

Assume, numbers

(since

Now it's up to us to choose constant

If values

For example, if values

Addressing our problem, we will have values

interval

interval

interval

interval

interval

interval

interval

interval

For number

Probabilities our random variable takes the above values are approximated by real frequencies of taking these values. Each such frequency is a ratio of the number of times this value occurred (

Now the mean value of our random variable is evaluated as

In this case it seems sufficient to approximate the mean as

Featured 9 months ago

One way to calculate the confidence interval of a sample mean is to use the student's t-distribution to find that with

One way to calculate the confidence interval of a sample mean is to use the student's t-distribution where the limits of the interval are given by:

where

First we need the sample mean and sample standard deviation:

and the sample standard deviation:

Plugging these values into our first equation we can calculate the limits of the confidence interval for our mean:

Where we can look up the value of

therefore we can say with

Featured 6 months ago

Answers bellow

a) the population proportion cannot be determined as that represents everyone. The sample, however, allows us to determine a point estimate,

The Point estimate is,

or in this case

b) to determine a confidence interval we use the equation,

where z is the z-score for your confidence level and

For a 95% confidence z= 1.959963985

so subbing into,

c) not sure exactly what you mean.

was think of using this equation but I'm not sure what you want to find out.

d) a smaller confidence interval 95%

A 95% confidence interval means that 95% of sample means taken will lie within this range. A 90% confidence interval means that 90% will lie within its range, which is smaller. For example,

95%

90%

The 90% confidence interval is smaller and thus we are less confident that the actual population mean lies within its range.

Featured 3 months ago

Let **Toothache** , and,

event that you have **Cavity** . Then,

you have **No Cavity.**

In the **Usual Notation** of **Conditional Probability** , we have,

Recall that,

Now,

Thus, from

are **mutually exclusive** events and

Therefore, by

Finally, the Reqd. Prob.

**Enjoy Maths.** , and, **spread** the **Joy!**

Featured 3 months ago

First let us look at the probability that the first card dealt is an ace and the other four non-aces...

There are

#4/52 = 1/13#

The remaining pack consists of

#48/51 = 16/17#

The probability of the third card being a non-ace is:

#47/50#

The probability of the fourth card being a non-ace is:

#46/49#

The probability of the fifth card being a non-ace is:

#45/48 = 15/16#

So the probability of an ace followed by

#1/13*color(red)(cancel(color(black)(16)))/17*47/50*46/49*15/color(red)(cancel(color(black)(16))) = 32430/541450 = 3243/54145#

The other four possible sequences of ace vs non-ace which result in exactly one ace being dealt are mutually exclusive, and will have the same probability as this first case.

So the probability of exactly one ace being dealt is:

#5 * 3243/54145 = 3243/10829#

Featured 3 weeks ago

From software:

From table lookup:

If we seek an 88% confidence interval, that means we only want a 12% chance that our interval does not contain the true value. Assuming a two-sided test, that means we want a 6% chance attributed to each tail of the

This

Find the closest value in the table to 0.9400 as you can, then see what its row and column is. From observation, we see that 0.9394 and 0.9406 are in the table with

**Note:** We could also get an answer from software like R, by typing the command

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