Solve the triangle if a = 11 and b = 80°.

step-by-step explanation:

in triangle abc

a=11

b=80

c=?

as we know sum of all the sides of a triangle is 180 degree by angle sum property

a+b+c=180 (asp)

11+80 +c=180

90 +c=180

c=180 -90

c=90

largest side is "b" =80

smallest side is "a" =11

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.