Suppose that the distribution for total amounts spent by students vacationing for a week in florida is normally distributed with a mean of 650 and a standard deviation of 120 . suppose you take a simple random sample (srs) of 15 students from this distribution. what is the probability that a srs of 15 students will spend an average of between 600 and 700 dollars? round to five decimal places.

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the total amounts spent by students vacationing for a week in Florida of a population, and for this case we know the distribution for X is given by:

Where and

And let represent the sample mean, the distribution for the sample mean is given by:

On this case  

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability on this way:

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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rauschg

rauschg · hand

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step-by-step explanation:

a precentage of 6th graders. the population is all 6th graders. let me know if i'm wrong, i hope this ! : )

step-by-step explanation: