In a recent study, the Centers for Disease Control and Prevention reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.6 and standard deviation 10. (a) Find the 10th percentile of the blood pressures. (b) Find the 34th percentile of the blood pressures. (c) Find the third quartile of the blood pressures. Use the TI-84 Plus calculator and round the answers to at least two decimal places.

A.) 67.78

B.) 76.48

C.) 87.34

Step-by-step explanation:

Given that:

Mean (m) = 80.6

Standard deviation (σ) = 10

A.) 10th percentile :

10th percentile corresponds to a Zscore of - 1.282

Zscore = (x - m) / σ

-1.282 = (x - 80.6) / 10

-12.82 = x - 80.6

x = -12.82 + 80.6

x = 67.78

B.)34th percentile of blood pressure ;

34th percentile corresponds to a Zscore of - 0.412

Zscore = (x - m) / σ

-0.412 = (x - 80.6) / 10

-4.12 = x - 80.6

x = - 4.12 + 80.6

x = 76.48

C.) third quartile = 75% = 0.75

75th percentile corresponds to a Zscore of 0.674

Zscore = (x - m) / σ

0.674 = (x - 80.6) / 10

6.74 = x - 80.6

x = 6.74 + 80.6

x = 87.34

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.