(i. The mean of a normal probability distribution is 60 and the standard deviation is 5. 95.44 percent of observations lie between 50 and 60. (ii) A z-value of -2.00 indicates that corresponding X value lies to the left of the mean.
(iii) One of the properties of the normal curve is that it gets closer to the horizontal axis, but never touches it. This property of the normal curve is called asymptotic.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (ii) and (iii) are correct statements but not (i).

Question

Quizplus · Accepted Answer

(i) is incorrect because 95.44 percent of observations lie within two standard deviations of the mean in a normal distribution, which would be between 50 and 70, not 50 and 60. (ii) is correct because a z-value of -2.00 does indeed indicate that the corresponding X value lies to the left of the mean in a standard normal distribution. (iii) is also correct because one of the properties of the normal curve is that it is asymptotic to the horizontal axis, meaning it approaches the axis infinitely but never actually touches it.

(I the Mean of a Normal Probability Distribution Is 60