Question

1. Find the total area under the standard normal curve to the left of z1 and to the right of z2.

z1 = -1.75, z2 = 1.89

a) 1.0224 b) 0.3231 c) 0.6769 d) 0.0695 e) 0.9305

2.Which of the following statements is false?

a) Normal distributions are symmetric, but they do not have to be bell-shaped.

b) The standard normal distribution is completely defined by its mean and standard deviation.

c) For any normal distribution, the mean, median, and mode are all equal.

d) The mean of the standard normal distribution is always 0.

Answer 1

1) To find P( Z < -1.75) + P( Z > 1.89)

= 0.0401 + 0.0294 = 0.0695

(This is found using Z-table for Normal distribution)

2) Normal distributions are symmetric, Bell shaped. The distribution is defined by its mean and standard deviation.

Normal distributions have equal mean, median and mode.

The standard normal distribution is one which has a mean equal to 0 and standard deviation equal to 1.

Thus, the statement in option (a) is false and hence the correct answer.