Sampling Distribution

A teacher believed that 25% of the students can get the highest marks in English mid- test.

If a random sample of 100 students selected,

a) What is the standard error of the sample proportion can get highest marks in English mid-test?

b) Calculate the probability that the sample proportion is exactly 0.20.

c) Calculate the probability that the sample proportion is less than 0.23

d) Calculate the probability that the sample proportion is greater than 0.19

e) Calculate the probability that the sample proportion is between 0.16 and 0.365

Reference :

*Z&T Table Distribution

https://drive.google.com/file/d/1nfSbQHR6k8Ri5ipEPBM1-4ZpLiMfKsvC/view?usp=sharing

KEY EQUATIONS Population Mean Finding X for the Sampling Distribution of the Mean X X =u+Z- Vn (7.5) u = (7.1) N Sample Proportion Population Standard Deviation P X (7.6) E(X; - 1)2 o (7.2) Standard Error of the Proportion N TT (1 - TT) Op = (7.7) Standard Error of the Mean n Vn (7.3) Finding Z for the Sampling Distribution of the Proportion P - TT Finding Z for the Sampling Distribution of the Mean Z = (7.8) TT (1 - TT) Z = - X - MX X -M (7.4) OX Vn The sampling distribution of mean The sampling distribution of mean proportion H x = H Mean of sample proportion = p Ox = = standard error 0 = bd n => standard error For finite population, o x= V-n N-1 Probability Z = p-p p ( 1 -p ) n Probability z = x- u or z = N - n VN-1