Mathematics, 02.04.2020 03:34 cache77

ACT mathematics score for a particular year are normally distributed with a mean of 27 and a standard deviation of 2 points

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Answer from: andrewmena05

A) the probability that a randomly selected score is greater than 29 points is 0.1587

B) The percentage of students scores are between 31 and 23 is 95.44%

C) A student who scores 31 is in the 97.72% percentile

Step-by-step explanation:

ACT mathematics score for a particular year are normally distributed with a mean of 27 and a standard deviation of 2 points.

Part A: What is the probability that a randomly selected score is greater than 29 points?

Part B: What percentage of students scores are between 31 and 23?

Part C: A student who scores 31 is in the ______ percentile.

A) Given that:

Mean (m) = 27 and standard deviation (s) = 2 points

Since the ACT mathematics score is normally distributed, we can use z score. To calculate Z score we use the equation:

$Z=\frac{x-m}{s}$

substituting values:

$Z=\frac{x-m}{s}==\frac{29-27}{2}=1\\Z=1\\$

P(X > 29) = P(Z > 1) = 1 - P(Z<1)

Using Z tables

P(X > 29) = P(Z > 1) = 1 - P(Z<1) = 1 - 0.8413 = 0.1587 = 15.87%

P(X > 29) = 0.1587

the probability that a randomly selected score is greater than 29 points is 0.1587

B) For score of 31

$Z=\frac{x-m}{s}==\frac{31-27}{2}=2\\Z=2\\$

For score of 23

$Z=\frac{x-m}{s}==\frac{23-27}{2}=-2\\Z=-2\\$

P(23 < X < 31) = P(-2 < Z < 2) = P(Z < 2) - P(Z < -2) = 0.9772 - 0.0228 = 0.9544

P(23 < X < 31) = 0.9544 = 95.44%

The percentage of students scores are between 31 and 23 is 95.44%

C) For score of 31

$Z=\frac{x-m}{s}==\frac{31-27}{2}=2\\Z=2\\$

P(X < 31) = P(Z < 2) = 0.9772 = 97.72%

A student who scores 31 is in the 97.72% percentile

Answer from: Quest

it would be 6xy and -16xy.

Answer from: Quest

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:

$\frac{little}{big} =\frac{side mn}{side ab}=\frac{side on}{side cb}$ .

$\frac{0.96}{1.2}=\frac{x}{3}$

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

$0.96(3)=1.2(x)\\2.88=1.2x\\\frac{2.88}{1.2}=\frac{1.2x}{1.2} \\2.4=x$

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