Mathematics, 28.09.2019 05:10 timothyallenhall2006

Auniversity found that 30% of its students withdraw without completing the introductory statistics course. assume that 20 students registered for the course. compute the probability that 2 or fewer will withdraw (to 4 decimals). compute the probability that exactly 4 will withdraw (to 4 decimals). compute the probability that more than 3 will withdraw (to 4 decimals). compute the expected number of withdrawals.

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Answer from: lisagrimmett3

Step-by-step explanation:

a) Compute the probability that 2 or fewer will withdraw

First we need to determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:

$(0.3)^2(0.7)^{18}$ .

Then, we must multiply this quantity by

${20\choose2}=\frac{20!}{18!2!}=\frac{20\times19}{2}=190,$

which is the number of ways to choose 2 students from the total of 20. Therefore:

the probability that exactly 2 students withdraw is $190(0.3)^2(0.7)^{18}$ .

Following an analogous process we can determine that:

The probability that exactly 1 student withdraw is ${20\choose1}(0.3)(0.7)^{19}=20(0.3)(0.7)^{19}.$ The probability that exactly none students withdraw is ${20\choose 0}(0.7)^{20}=(0.7)^{20}.$

Finally, the probability that 2 or fewer students will withdraw is

$190(0.3)^2(0.7)^{18}+20(0.3)(0.7)^{19}+(0.7)^{20}=(0.7)^{18}(190(0.3)^2+20(0.3)(0.7)+(0.7)^2)\approx0.0355$

b) Compute the probability that exactly 4 will withdraw.

Following the process explained in a), the probability that 4 student withdraw is given by

${20\choose4}(0.3)^4(0.7)^{16}=\frac{20\times19\times18\times17}{4\times3\times2} (0.3)^4(0.7)^{16}=4845(0.3)^4(0.7)^{16}\approx 0.1304.$

c) Compute the probability that more than 3 will withdraw

First we will compute the probability that exactly 3 students withdraw, which is given by

${20\choose3}(0.3)^3(0.7)^{17}=\frac{20\times19\times18}{3\times2} (0.3)^3(0.7)^{17}=1140(0.3)^3(0.7)^{17}\approx 0.0716.$

Then, using a) we have that the probability that 3 or fewer students withdraw is 0.0355+0.0716=0.1071. Therefore the probability that more than 3 will withdraw is 1-0.1071=0.8929

d) Compute the expected number of withdrawals.

As stated in the problem, 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.

Answer from: Quest

(-1,-0.5)

step-by-step explanation:

Answer from: Quest

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

Identify the transformation that maps the figure with center (7, 1) onto itself. a) rotate 180° cloc

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Auniversity found that 30% of its students withdraw without completing the introductory statistics c...