Question

6.A population has a mean of μ = 60 and a standard deviation of σ = 12.

a.For the population, find the z-score for each of the following X values.

X = 69: z =_____X = 84: z =_____X = 63: z =_____

X = 54: z =_____X = 48: z =_____X = 45: z =_____

b.For the same population, find the score (X value) that corresponds to each of the following z-scores.

z = 0.50: X=_____ z = 1.50: X=_____z = -2.50: X=_____

z = -0.25: X=_____z = -0.50: X=_____z = 1.25: X=_____

7. A sample has a mean of M = 30 and a standard deviation of s = 8. Find the z-score of for each of the following X values from this sample.

X = 32: z =_____X = 34: z =_____X = 36: z =_____

X = 28: z =_____X = 20: z =_____X = 18: z =_____

8. A sample has a mean of M = 25 and a standard deviation of s = 5. For this sample, find the X value corresponding to each of the following z-scores.

z = 0.40: X=_____z = 1.20: X=_____z = 2.00: X=_____

z = -0.80: X=_____z = -0.60: X=_____z = -1.40: X=_____

Answer 1

Q6 )

Given,

Mean = = 60

Standard deviation = = 12

Formula for z score :

z = ( X - mean ) / Standard deviation

a)

We have to find z scores for given values of x.

i) X = 69

ii)

X = 84

iii )

X = 63

iv)

X = 54

v)

X = 48

vi)

X = 45

b)

We have to find X value for given z-scores.

i)

z = 0.50

ii)

z = 1.50

iii)

z = -2.50

iv)

z = -0.25

v)

z = -0.50

vi)

z = 1.25

Q7)

Given ,

Mean M= 25 ( Estimate of )

Standard deviation S= 5 ( Estimate of )

z = ( X - mean ) / Standard deviation

We have to find z scores for given values of x.

i)

X = 32

ii)

X = 34

iii)

X = 36

( similarly solve next )

Q8)

Given ,

Mean M= 25 ( Estimate of )

Standard deviation S= 5 ( Estimate of )

We have to find X value for given z-scores.

i)

z = 0.40

ii)

z = 1.20

iii)

z = 2.00

( similarly solve next )