A normal distribution has a mean of 137 and a standard deviation of 7. Find the z-score for a data value of 121. Incorrect Round to two decimal places g

The z-score for a data value of 121 is -2.29.

Step-by-step explanation:

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find the z-score for a data value of 121.

This is Z when X = 121. So

The z-score for a data value of 121 is -2.29.

.

Step-by-step explanation:

We have been given that a normal distribution has a mean of 137 and a standard deviation of 7. We are asked to find the z-score corresponding to data value 121.

We will use z-score formula to solve our given problem.

, where,

z = Z-score,

x = Sample score,

= Mean,

= Standard deviation.

Upon substituting our given values in above formula, we will get:

Upon rounding to two decimal places, we will get:

Therefore, z-score corresponding to data value 121 would be .

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!