Sampling Distribution

1. Mean and standard deviation population weight of male students is 68 kg and 3 kg.

If a sample size of 25 was used, calculate the standard deviation of the sample.

2. Payment of research assistants for one hour is normally distributed with mean of $13 and variance $81. Determine the probability the payments sample size of 300 research assistants which is between $12.80 to $14.50.

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