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1. A box contains 5 red and 7 non-red balls. Three are selected randomly, all at once.

X is the number of red balls selected.

a) Write the distribution of X. Express the probabilities as fractions.

b) Show all work to find E(X). X is not a binomial random variable. You must show the work.

c) Use your calculator to find the standard deviation of X.

2. The probability a certain fungicide will cure an infected plant is found to be 0.75. Eighty infected plants are treated. X is the number of plants which are cured.

a) Find the expected value and standard deviation of X. Round to 3 decimal places.

b) Find the probability that X is equal to the expected value found in a.

c) Find the probability that X is between 57 and 63 inclusive. Round to 5 decimal places.

d) Find the normal approximation to the probability in c, rounded to 5 decimal places.

3. Heights of a certain population of males are normally distributed with mean 70 inches and standard deviation 2 inches.

a) Find a height, h, so that the probability a male is shorter than h is 0.3. Round to 2 decimal places.

b) Find a height, H, so that the probability a male is taller than H is 0.8.. Round to 2 decimal places.

4. X is a normal random variable with mean 40 and unknown standard deviation.

It is known that P(X< 55) = 0.65. Use symmetry to find P(25 < X < 55).