Question

A random sample of 100 students is taken from the population of all part-time students in the U.S., for which the overall population of females is 0.60.6. Start by determining what is given in the original statement.

Probabilities: Proportion Sampling Distributions If a sampling distribution is normally shaped, we can apply the Empirical Rule and use Z-scores to determine probabilities. Let's look at some examples. Example A random sample of 100 students is taken from the population of all part-time students in the U.S., for which the overall population of females is 0.6. Start by determining what is given in the original statement. 100 = n 0.6 = P Test to see if we can use the normal distribution. np = 60 and ng = Can we use the normal approximation? Yes, np and ng are both greater than 10 - = (Hint: Since the population proportion is p = 0.6, we know the mean of the sampling proportions is Mp Mp = p.) PG What is the standard deviation? op (Round to the nearest thousandth.) Hint: 0; = 72

Answer 1

n = sample size of students = 100

p = proportion of females = 0.6

np = 100 * 0.6 = 60

nq = 100 * (1-0.6) = 100 * 0.4 = 40

Normal Approximation can we applied since n>=10 and p is close to 0.5

If Normal approximation is applied for X, then

mean of binomial = np, variance of binomial = npq

X - N(np, npq) => X ~ N(60, 24)

mean of sample proportions is equal to population proportion = p̂ = P = 0.6

standard deviation is equal to squre root of (p*q)/n = square root of (0.6*0.4)/100 = square root of 0.0024 = 0.0489