Based on the Normal model N(100,17) describing IQ scores, what percent of individuals would be expected to have scores a) over 80? b) under 89? c) between 111 and 131? d) over 128?

a) 88.10% of students would be expected to score over 80

b) 25.78% of students would be expected to score under 89.

c) 22.34% of students would be expected to score between 111 and 131.

d) 4.95% of students would be expected to score over 128.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

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:

a) over 80?

1 subtracted by the pvalue of Z when X = 80.

has a pvalue of 0.1190

1 - 0.1190 = 0.8810

88.10% of students would be expected to score over 80

b) under 89?

Pvalue of Z when X = 89. So

has a pvalue of 0.2578.

25.78% of students would be expected to score under 89.

c) between 111 and 131?

Pvalue of Z when X = 131 subtracted by the pvalue of Z when X = 111.

X = 131

has a pvalue of 0.9656.

X = 111

has a pvalue of 0.7422.

0.9656 - 0.7422 = 0.2234

22.34% of students would be expected to score between 111 and 131.

d) over 128?

1 subtracted by the pvalue of Z when X = 128. So

has a pvalue of 0.9505

1 - 0.9505 = 0.0495

4.95% of students would be expected to score over 128.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

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step-by-step explanation:

if the four friends split the cost, p, of the pizza evenly, then each friend pays one-fourth of the cost of the pizza.

the expression is   or