Question

* Select all the True statements about the normal probability distribution.*

a) The random variable takes any value.

b) The distribution has one mode and has positive skew

c)The mean, median, and mode are equal.

d) Standardizing an observation of any normal distribution allows the use of the standard normal (Z) distribution tables.

e) The distribution has one mode and is bell shape.

f) The area under the bell curve is 1 exactly.

g) The random variable does not take any value. It takes discrete value like the binominal distribution.

Answer 1

a) The random variable takes any value. - True - The range of X is from to

b) The distribution has one mode and has positive skew. - False. Skewness is 0 and the distribution is symmetrical.

c)The mean, median, and mode are equal. - True

d) Standardizing an observation of any normal distribution allows the use of the standard normal (Z) distribution tables. - True

e) The distribution has one mode and is bell shape. - True

f) The area under the bell curve is 1 exactly. - True because the area under the curve is the probability of the distribution over all possible range of x which should always be 1.

g) The random variable does not take any value. It takes discrete value like the binominal distribution. False - The normal distribution is a continuous distribution and not discrete distribution.