Question

The scaled test scores for the New York State Grade 8 English Language Arts Test are normally distributed. The normal curve shown below represents this distribution. What is the mean test score? Estimate the standard deviation of this normal distribution. (Adapted from New York State Education Department) a. Find the line of symmetry and identify the mean. b. Estimate the inflection points and identify the standard deviation.

Answer 1

As you haven't provide any of the figure on which i can show you the mean sd. Inflection point

But I've drawn a figure for you

From which you can relate easily

Here the mean is the middle value on the curve which divides the curve symmetrically.

In the figure a line is drawn in middle of curve

At 80 which divides curve symmetrically , so u = mean = 80

Here upward arrows shows upward curve and down arrows shows downward curve which is darken too.

From 20 to 60 curve is upward sloping and at 60 curve changes the direction and making inward till 100, after 100 is again changes direction and makes outward curve

These two changing points are A and B, and this is called Inflection point of normal curve.

In a nornal distribution the point at which the graph changes from curving upward to downward and from downward to upward and is called Inflection point of curve

Now standard deviation

As inflection point is above 20 and below 20 points from mean, at 100 and 60 respectively.

So we can say that curve has a standard deviation of 20 (approximately).

And line of symmetry is line on which curve folds itself

That is middle line on 80 as shown in diagram.

From this you can relate your curve and find everything.

As you haven't posted curve photo

That is all i can do for you

Rate good .... Thanks...:)