A farmer uses artificial insemination to impregnate his cows. This method has an 80% success rate. • Suppose 100 cows are selected at random to be inseminated. Find the mean and standard deviation of this binomial distribution. • Suppose 100 cows are selected at random to be inseminated. Use the normal approximation to the binomial distribution to find the probability that 75 or more cows become pregnant.

About 78% of all female heart transplant patients will survive for at least 3 years seventy female transplant patients are randonly selected. What is the probability that the sample proportion surving for at least 3 years will be less than 72%? Assume the sampling distribution of sample proportions is a normal distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to pq/n. The probability that the sample proportion surviving for at least 3 years will be less than 72% is ____________. Round answer to four decimal places.

Assume that the square footage of a residential house in the US is normally distributed with a mean=1000 and standard deviation=150 square feet. If we select a random house what is the probability that it will be at most 1050 square feet?

Explain how the special formulas for the mean and standard deviation of a binomial or Poisson random variable are derived.