Question

Select True or False from each pull-down menu, depending on whether the corresponding statement is true or false.

  ?    True    False      1. Using the standard normal curve, the z−z−score representing the 90th percentile is 1.28.

  ?    True    False      2. The mean and standard deviation of a normally distributed random variable which has been standardized are one and zero, respectively.

  ?    True    False      3. A random variable XX is normally distributed with a mean of 150 and a variance of 36. Given that X=120X=120, its corresponding z−z− score is 5.0

  ?    True    False       Let z1z1 be a z−z− score that is unknown but identifiable by position and area. If the area to the right of z1z1 is 0.8413, the value of z1z1 is 1.0

My answer was

1. T

2. T

3.F

4. T

but I didnt get credit for that so I think there is something wrong

Answer 1

Solution:-

Given that,

1) Using standard normal table,

P(Z < z) = 90%

= P(Z < z) = 0.90  

= P(Z < 1.28) = 0.90

z = 1.28

True

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

mean = 0, standard deviation = 1

False

3) mean = = 150

variance = ² = 36  

standard deviation =   = ² = 36 = 6

x = 120

Using z-score formula,

z = x - /   

z = 120 - 150 / 6

z = -5.00

False

4) P( Z > z1 ) = 0.8413

= 1 - P( Z < z1 ) = 0.8413

= P( Z < z1 ) = 1 - 0.8413

= P( Z < z1 ) = 0.1587

= P( Z < -1.00 ) = 0.1587

z1 = -1.00

False