Normal Approximations to Binomial Distributions

For a binomial distribution: n = the number of

independent trials p = the probability of

success q = the probability of failure µ = np σ = √npq

TWO conditions:np > 5 and nq

> 5

If conditions are met, then the random variable x is normally distributed.

Binomial distributions are DISCRETE, but the normal distribution is CONTINUOUS.

The binomial probability formulas from CH 4 are for exact probabilities. i.e., P(X = 4)

To adjust for continuity, move 0.5 units to the left and right of the midpoint. This allows you to include all x-values in the interval. i.e., P(3.5 < X < 4.5)

1. The probability if getting between 39 and 77 successes, inclusive.

2. The probability of getting at least 80 successes.

3. The probability of getting fewer than 50 successes.

1. Find n, p, and q2. Is np > 5? Is nq > 5?3. Find µ and σ4. Correct for Continuity (+ 0.5)5. Find z6. Use standard normal table to

finish

24. A survey of US adults ages 50-64 found that 70% use the Internet. You randomly select 80 adults ages 50-64 and ask them if they use the Internet.

A. Find the prob that at least 70 people say they use the Internet.

B. Find the prob that exactly 50 people say they use the internet.

C. Find the prob that more than 60 people say they use the internet.

25. About 34% of workers in the US are college graduates. You randomly select 50 workers and ask them if they are a college graduate.

A. Find the prob that exactly 12 workers are college graduates.

B. Find the prob that more than 23 workers are college graduates.

C. Find the prob that at most 18 workers are college graduates.

D. A committee is looking for 30 working college graduates to volunteer at a career fair. The committee randomly selects 125 workers. What is the probability that there will not be enough college graduates?