Question

Suppose there is a normally distributed population which has a mean of μ = 440and a standard deviation of σ = 60. (15p)

1.What portion of a normal distribution is below 295?

2. What z-score would correspond to a raw score of 260?

3. What raw score would correspond to a z score of -3.5?

4. If we randomly select one score from this population, what is the probability that will be less than 550?

5. If we randomly select one score from this population, what is the probability that will be greater than 580?

Answer 1

Solution :

Given that ,

mean = = 440

standard deviation = = 60

1) P(x < 295) = P[(x - ) / < (295 - 440) / 60]

= P(z < -2.42)

Using z table,

= 0.0078

2) x = 260

Using z-score formula,

z = x - /   

z = 260 - 440 / 60

z = -3.00

3) z = -3.5

Using raw-score formula,

x = z * +

x = -3.5 * 60 + 440

x = 230

4) P(x < 550) = P[(x - ) / < (550 - 440) / 60]

= P(z < 1.83)

Using z table,

= 0.9664

5) P(x > 580 ) = 1 - p( x< 580)

=1- p P[(x - ) / < (580 - 440) / 60 ]

=1- P(z < 2.33)

Using z table,

= 1 - 0.9901

= 0.0099