A six-sided die is rolled four times. Let the random variable x count the number of 6's that are rolled. 1) Show that this process is a binomial process by verifying the four conditions. 2) Calculate the flowing probabilities (round to 3 decimal places): a) P(x = 0) b) P(x = 1) c) P(x = 2) d) P(x = 3) e) P(x = 4)

3) Use your answers from #2 to create a probability distribution for this random variable. x P(x)

4) Use the probability distribution to calculate the probability of rolling an even number of 6's. 5) Use the probability distribution to calculate the probability of rolling at least one 6. 6) Calculate , 2, and . Remember, this is a binomial probability distribution.

Women's heights are normally distributed with a mean of 63.4 inches and a standard deviation of 2.8 inches. Calculate the following: 7) P(62.3 < x < 64.9) 8) P(x > 64.9) 9) P(x < 58.6) 10) Determine the height, in inches, that separates the tallest 5% of women from the rest. Round to one decimal place.