Mathematics, 08.07.2019 18:00 lailabirdiemae

What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the critical reading part of the test (to 4 decimals)? 0.6578?

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Given that the College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) ( The World Almanac , 2009):

Critical Reading 502
Mathematics 515
Writing 494

Assume that the population standard deviation on each part of the test is σ = 100.

We find the probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the critical reading part of the test (to 4 decimals) as follows:

Within 10 points of 502 implies (502 - 10, 502 + 10) = (492, 512).

Because the sample is large, we assume normal distribution.

The probability that the mean statistic of sample data is between two points (a, b) is given by:

$P(a\ \textless \ \bar{x}\ \textless \ b)=P\left( \frac{b-\mu}{\sigma/\sqrt{n}} \right)-P\left( \frac{a-\mu}{\sigma/\sqrt{n}} \right)$

Thus,

$P(492\ \textless \ \bar{x}\ \textless \ 512)=P\left( \frac{512-502}{100/\sqrt{90}} \right)-P\left( \frac{492-512}{100/\sqrt{90}} \right) \\ \\ = P\left(\frac{10}{10.5409} \right)-P\left(\frac{-10}{10.5409} \right)=P(0.9487)-P(-0.9487) \\ \\ =P(0.9487)-[1-P(0.9487)]=2P(0.9487)-1=2(0.82861)-1 \\ \\ =1.65722-1=0.65722$

Therefore, the probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the critical reading part of the test (to 4 decimals) is 0.6572.

Answer from: Quest

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

Answer from: Quest

c) the median for town a 30" is greater than the median for town b 25"

step-by-step explanation:

town a, median = q2 = 30

town b, median - q2 = 25

so the median for town a 30" is greater than the median for town b 25"