1. Solve for X using Z (hint: there is a formula for that in your slides!). A normal distribution has mew =45 and sigma =7. What is the minimum raw score X needed to be in the top 4.0% of the distribution? (hint: find the Z score that corresponds to the proportion in the tail = to 4.0%). (2 points)

1. What proportion of a normal distribution is located in the tail beyond z = 2.13?

1. What proportion of a normal distribution is located between the mean and z = -0.79?

1. What proportion of a normal distribution is located between the mean and z = 1.16?

1. The normal distribution is divided into two pieces at z = 0.38. What proportion of the distribution is on the right-hand side of the line?

1. The normal distribution is divided in two pieces at z = 1.55. What proportion of the distribution is on the left-hand side of the line? (hint: it will really help to draw this and shade the left hand side of the line!)

1. What Z score values represent the lowest 4% and the highest 4% of the distribution?

1. What z-score values form the boundaries for the middle 80% of a normal distribution (hint: if you put 90% of the distribution in the middle, how much is left in each tail)?

1. SAT scores are normally distributed with a mean of = 500 with = 50. If the state college only accepts students who score in the top 70% on the SAT, what is the minimum score needed to be accepted? Hint: sketching a graph and visually representing the top 70% will help.