Question

Give all answers to 4 decimal places.

For a standard normal distribution:

a) find the probability a score is between the mean and 0.85 standard deviations above the mean?    

b) find the probability a score is between the mean and 0.85 standard deviations below the mean?    

c) If the probability that a person scores below a particular value is 0.17, then the probability a person scores above that value equals?     

d) If the probability that a person scores between a particular positive z value and the mean is 0.2, then the probability a person scores above that value equals?

Answer 1

a) find the probability a score is between the mean and 0.85 standard deviations above the mean?   

Solution:

We have to find P(0<Z<0.85)

P(0<Z<0.85) = P(Z<0.85) – P(Z<0) = 0.802337 – 0.5 = 0.302337

Required probability = 0.3023

b) find the probability a score is between the mean and 0.85 standard deviations below the mean?

We have to find P(-0.85<Z<0)

P(-0.85<Z<0) = P(Z<0) – P(Z<-0.85) = 0.5 - 0.197663 = 0.302337

Required probability = 0.3023

c) If the probability that a person scores below a particular value is 0.17, then the probability a person scores above that value equals?     

We are given P(Z<z) = 0.17

We have to find P(Z>z)

P(Z>z) = 1 – P(Z<z) = 1 – 0.17 = 0.83

Required probability = 0.8300

d) If the probability that a person scores between a particular positive z value and the mean is 0.2, then the probability a person scores above that value equals?

We are given P(0<Z<z) = 0.2

We have to find P(Z>z) = 0.5 – 0.2 = 0.3

Required probability = 0.3000