Normal Approximations to Binomial Distributions.  For a binomial distribution:  n = the number of independent trials  p = the probability of success.

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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 > 5and 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 q 2. Is np > 5? Is nq > 5? 3. Find µ and σ 4. Correct for Continuity (+ 0.5) 5. Find z 6. Use standard normal table to finish

 24. A survey of US adults ages found that 70% use the Internet. You randomly select 80 adults ages 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?