Scores in the game of Marbelite follow a normal distribution with a mean of 76 and a standard deviation of 11. vishwas plays marbelite and is an average player; he feels his scores will fall in the middle 64.24% of the distribution. between what two scores must viswas have in the game of marbelite to fall in the middle of 64.24% of the distribution

And if we solve for a we got

So the value of height that separates the bottom 17.88% of data from the top 82.12% is 65.88.

And for the other value we can use z = 0.920 since the distribution is symmetric, and we got:

So the two values for this case who accumulate 64.24% of the area are (65.88; 86.12)

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 scores of a population, and for this case we know the distribution for X is given by:

Where and

And we want 0.6424 of the area between two values. So then we have on the tails (1-0.6424)/2 = 0.1788 of the area.

For this part we want to find a value a, such that we satisfy this condition:

  (a)

  (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.1788 of the area on the left and 0.8212 of the area on the right it's z=-0.920. On this case P(Z<-0.920)=0.1788 and P(z>-0.920)=0.8212

If we use condition (b) from previous we have this:

But we know which value of z satisfy the previous equation so then we can do this:

And if we solve for a we got

So the value of height that separates the bottom 17.88% of data from the top 82.12% is 65.88.

And for the other value we can use z = 0.920 since the distribution is symmetric, and we got:

So the two values for this case who accumulate 64.24% of the area are (65.88; 86.12)

answer is : muchas/tipicas

have a nice day!

~recklesschicken