91Ó°ÊÓ

The values of the sample proportion $pˆ$ of red beads are approximated well by a Normal distribution with mean of $0.75$ and standard deviation of $0.06$.

Individuals who are being examined make up the population.

A huge container contains POPULATION $=4000$beads, $1000$of which are white and $3000$of which are red.

The population distribution is approximately a binomial distribution with $p=\frac{3000}{4000}=0.75$(proportion of red beads).

The values of the sample proportion $pˆ$of red beads are approximated well by a Normal distribution with mean of $0.75$ and standard deviation of $0.06$.

The sample proportion $\hat{p}$values are distributed normally, with a mean of $0.75$and a standard deviation of $0.06$.

As a result $\hat{p}$'s sampling distribution is the Normal distribution, with a mean of $0.75$and a standard deviation of $0.06$.

The proportion of red beads in a sample of size $50$is described by the sampling distribution of $\stackrel{¯}{x}$Its difference distribution distinguishes it from the population distribution (Normal instead of binomial).