<span>No, because the mean is larger in the social studies book</span>
Take the area of the rectangle as a whole and subtract the triangle piece.
We know the dimensions of the triangle are 3x4 so you can multiply it out using the formula to find the triangle's area to get 6.
Then you calculate the area of the whole rectangle. 10x12=120.
Finally subtract the triangle from the rectangle. 120-6=114.
The Area of the deck is 114.
A. P(492 < x-bar < 512)
<span>z = (492-502)/100/√90 </span>
<span>z = -0.95 is 0.1711 </span>
<span>z = (512-502)/100/√90 </span>
<span>z = 0.95 is 0.8289 </span>
<span>b. P(505 < x-bar < 525) </span>
<span>z = (505-515)/100/ √90 </span>
<span>z = -0.95 </span>
<span>z = (525-515)/100/ √90 </span>
<span>z = 0.95 </span>
<span>P(-0.95< z < 0.95) = 0.6578 </span>
<span>P(-0.95< z < 0.95) = 0.6578 </span>
<span>c. P(484 < x-bar < 504) </span>
<span>z = (484-494)/100/√100 </span>
<span>z = -1 is 0.1587 </span>
<span>z = (504-494)/100/√100 </span>
<span>z = 1 is 0.8413 </span>
<span>P(-1< z <1) = 0.6826</span>
There are 4 positions in the string that each have 25 choices (any letter in the English alphabet except A) and the other positions are filled with A, so there are 25⁴ possible strings containing exactly 7 A's.
Overall, there are 26¹¹ possible strings of length 11.
Then the probability of randomly generating a string containing exactly 7 A's is
25⁴ / 26¹¹ ≈ 0.000000000106427
