PLEASE help with Probaility Problem?

At a university, 60% of the 7499 students are female. The student new paper reports results of a survey of a random sample of 50 students about various topics invinvolvingcohol abuse, such as participation in binge drinking. They report that their sample contained 26 females





a) Explain how you can set up a binary random variable X to represent gender





b) Identify the population distribution of gender at this university





c) Identify the data distribution gender for this sample





D) Identify the sampling distribution of the sample proportion of females i the sample.


State its mean and standard error for a random sample of size 50|||n = 50; p = 0.6; q = 0.4; x = 30


渭 = (n p) = 30; 蟽虏 = ( n p q ) = 12; 蟽 = 鈭? n p q ) = 3.4641


x P(x) 危P(x) 1-危P(x)


--- --------- --------- ---------


0 0.0000000 0.0000000 1.0000000


1 0.0000000 0.0000000 1.0000000


2 0.0000000 0.0000000 1.0000000


3 0.0000000 0.0000000 1.0000000


4 0.0000000 0.0000000 1.0000000


5 0.0000000 0.0000000 1.0000000


6 0.0000000 0.0000000 1.0000000


7 0.0000000 0.0000000 1.0000000


8 0.0000000 0.0000000 1.0000000


9 0.0000000 0.0000000 1.0000000


10 0.0000000 0.0000000 1.0000000


11 0.0000000 0.0000000 1.0000000


12 0.0000002 0.0000002 0.9999998


13 0.0000009 0.0000011 0.9999989


14 0.0000035 0.0000046 0.9999954


15 0.0000125 0.0000171 0.9999829


16 0.0000410 0.0000581 0.9999419


17 0.0001230 0.0001811 0.9998189


18 0.0003382 0.0005193 0.9994807


19 0.0008545 0.0013738 0.9986262


20 0.0019866 0.0033604 0.9966396


21 0.0042570 0.0076174 0.9923826


22 0.0084173 0.0160348 0.9839652


23 0.0153708 0.0314056 0.9685944


24 0.0259382 0.0573438 0.9426562


25 0.0404636 0.0978074 0.9021926


26 0.0583610 0.1561683 0.8438317


27 0.0778146 0.2339830 0.7660170


28 0.0958787 0.3298617 0.6701383


29 0.1091034 0.4389651 0.5610349


30 0.1145586 0.5535236 0.4464764


Normal Approximation:


z = ( x - 渭 ) / 蟽


P ( x %26lt; 29.5) = P ( z %26lt; -0.1443 ) = 0.4426


P (29.5 %26lt; x %26lt; 30.5) = P (-0.1443 %26lt; z %26lt; 0.1443) = 0.1148


P (30.5 %26lt; x ) = P (0.1443 %26lt; z ) = 0.4426