Answer:
Step-by-step explanation:
Given that the height in inches, of a randomly chosen American woman is a normal random variable with mean μ = 64 and variance 2 = 7.84.
X is N(64, 2.8)
Or Z = ![\frac{x-64}{2.8}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-64%7D%7B2.8%7D)
a) the probability that the height of a randomly chosen woman is between 59.8 and 68.2 inches.
![=P(59.8](https://tex.z-dn.net/?f=%3DP%2859.8%3CX%3C68.2%29%5C%5C%3D%20P%28%7CZ%7C%3C1.5%29%5C%5C%3D0.8664)
b) ![P(X\geq 59)\\= P(X\geq -1.78)\\ \\=0.9625](https://tex.z-dn.net/?f=P%28X%5Cgeq%2059%29%5C%5C%3D%20P%28X%5Cgeq%20-1.78%29%5C%5C%20%5C%5C%3D0.9625)
c) For 4 women to be height 260 inches is equivalent to
4x will be normal with mean (64*4) and std dev (2.8*4)
4x is N(266, 11.2)
![P(4x>260)= \\P(Z\geq -0.53571)\\=0.7054](https://tex.z-dn.net/?f=P%284x%3E260%29%3D%20%5C%5CP%28Z%5Cgeq%20-0.53571%29%5C%5C%3D0.7054)
d) Z is N(0,1)
E(Z19) = ![P(Z>19)\\= 0.000](https://tex.z-dn.net/?f=P%28Z%3E19%29%5C%5C%3D%200.000)
since normal distribution is maximum only between 3 std deviations form the mean on either side.
3.1 x 10^10
Yeah, that's it.
1/19 and then to draw a green marble would have to be 1/18 so I hope that helps