Help with Statistics Question?

Question

Here is the question I am having troubling figuring out how to solve.

A recent study by the Island Resort Taxi Drivers Association showed that the mean fare charged for service from the beach to the airport is $18.00 and the standard deviation is $3.50. We select a sample of 15 fares.

a) What is the likely hood that the sample mean is between $17 and $20?
b) what do we have to assume to make the above calculation?

Any help just to get me started would be greatly Appreciated

Answer 1

So they gave you the standard deviation of the population, what you need to do is calculate the stanard deviation (std error) of the sample mean, which is:

(std dev)/sqrt(n)

z = (sample mean - 18.00)/std error, you plug in 17 and then also 20 for the sample mean value to get the lower and upper z values.

you could also do the same for the t distribution with df = n - 1, and use the t table.

With use of the t table you assume a normal distribution, but with either case you want something at least mound shaped and symmetrical for this low a value of n, the number of samples units. I would use the t.

Answer 2

I'll help you.

In statistics, if you have a "normally distributed" population, then you can start to extrapolate how far from the mean each value is.

So for your questions:

a) Fares within one standard deviation will be between $14.50 and $21.50. These two fares are simply the mean +/- one standard deviation ($3.50).

Now, in a normally distributed population, 68.27% of the values will lie within one standard dev, 95.44% within two, and 99.73 within three standard deviations.

What is the likelihood that the sample mean is between $17 and $20? Since both of those means is within one standard deviation of $18, then the likelihood is 68.27%.

b) You have to assume that the population is normally distributed.

Regards,

Mysstere

Answer 3

You need to assume a normal distribution.

ans. to your prob is .328597

There are tables and programs for this. Try davidmlane.com-z table

Regards