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)

x + 4/7

step-by-step explanation:

use cymath

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.