Question

Select True or False 1. A random variable X is normally distributed with a mean of 150 and a variance of 36. Given that X = 120, its corresponding z− score is 5.0 __________ 2. 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________ 3. The mean and standard deviation of a normally distributed random variable which has been standardized are one and zero, respectively._______

Answer 1

Answer:

False, true, false

Step-by-step explanation:

We know that a random variable is symmetrical about the mean, unimodal, with more than 99% lying within 3 std deviations from the mean.

Using the std normal variate as Z = N(0,1) we can convert any normal variate to std normal variate and find the area/probability

Here X is N(120,36)

a, Given that X = 120, its corresponding z− score is 5.0 __________

Corresponding Z score is $\frac{120-150}{36} =-0.833$

Hence given statement is False

2. 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. Because we have between 0 and 2 area = 0.4772 so two times is 0.9544

3. The mean and standard deviation of a normally distributed random variable which has been standardized are one and zero, respectively._______

False because mean is 0 and std dev is 1.