A standardized exam's scores are normally distributed. In a recent year, the mean test score was 21.4 and the standard deviation was 5.5. The test scores of four students selected at random are 13, 24, 10, and 36. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 13 is nothing. (Round to two decimal places as needed.)

-1.53

0.47

-2.07

2.65

The last two observations are unusual

Step-by-step explanation:

mathematically;

z-score =( x-mean)/SD

Kindly note that an observation is termed unusual if the z-score is greater than +2 or less than -2

for x= 13

z-score = (13-21.4)/5.5 = -1.53

for x= 24

z-score= (24-21.4)/5.5 = 0.47

for x = 10

z-score = (10-21.4)/5.5 = -2.07

unusual

for x = 36

z-score = (36-21.4)/5.5 = 2.65

unusual

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

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step-by-step explanation:

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