Question

Select True or False depending on whether the corresponding statement is true or false. 1. Let z1 be a z− score that is unknown but identifiable by position and area. If the area to the right of z1 is 0.8413, the value of z1 is 1.0 2. The mean and standard deviation of an exponential random variable are equal to each other. 3. Using the standard normal curve, the z−score representing the 90th percentile is 1.28. 4. 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

Answer 1

Solution:

Question 1) Let z1 be a z− score that is unknown but identifiable by position and area.

If the area to the right of z1 is 0.8413, the value of z1 is 1.0

That is it means:

P( Z > 1.00 ) = 0.8413

but in fact P(Z < 1.0)= 0.8413

Above table gives area left of z value and thus we have: P( Z < 1.00) = 0.8413

Thus given statement is FALSE.

Question 2) The mean and standard deviation of an exponential random variable are equal to each other.

TRUE

Mean and  Standard Deviations for exponential distribution are equal and it is:

Question 3)  Using the standard normal curve, the z−score representing the 90th percentile is 1.28

Look in z table for area = 0.9000 or its closest area and find z value:

Area 0.8997 is closest to 0.9000 and it corresponds to 1.2 and 0.08

thus z = 1.28

Thus given statement is TRUE.

Question 4) 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

Thus standard deviation =

z score formula is:

This is negative , but statement says 5.00, thus given statement is FALSE