A jar contains 10 black marbles and 40 white marbles.

a. If you randomly select a marble from the jar, what is the probability that you will get a white marble?

b. If you are selecting a random sample of n = 3 marbles, and the first 2 marbles are both white, what is the probability that the third marble will be black?

For each of the following z-scores, sketch a normal distribution and draw a vertical line at the location of the z-score. Then, determine whether the body is to the right or the left of the z-score and find the proportion of the distribution located in the body.

a. z = -0.33 c. z = 1.96

b. z = 0.75 d. z = -0.67

The distribution of scores on the SAT test is approximately normal with = 500 and = 100.

a. What proportion of the population have SAT scores above 575?

b. What proportion of the population have SAT scores below 520?

c. What is the minimum SAT score needed to be in the highest 30% of the population?

d. What SAT score separates the top 65% from the rest of the distribution?