Suppose x is normally distributed with a mean of 75 and a standard deviation of 4. Would it be unusual to observe a value x = 59 or less? Explain (how many standard deviations below the mean; what's the corresponding z-score? What is the probability of x <= 59?).
2. Suppose x is normally distributed with a mean of 75 and a standard deviation of 4.
a. Find the 90th percentile.
b. Find the 95th percentile.
c. Find the 5th percentile.
4. Using the standard normal curve, the probability or area between z = -1.28 and z = 1.28 is 0.3997. True-False?
5. Let ^z1 be a z-score that is unknown but identifiable by position and area. If the symmetrical area between -^z1 and +^z1 is 0.9544, the value of ^z1 is 2.0. True-False?
6. The z-score representing the first quartile of the standard normal distribution is:
a. 0.67
b. -0.67
c. 1.28
d. -1.28
e. 0.28