Question

What is the z-score of

x = 4,

if it is 0.199 standard deviations to the left of the mean? (Enter an exact number as an integer, fraction, or decimal.)
z =

Suppose

X ~ N(11, 1).

What value of x has a z-score of −4.25? (Enter an exact number as an integer, fraction, or decimal.)
x =

Suppose

X ~ N(6, 5).

What value of x is three standard deviations to the right of the mean? (Enter an exact number as an integer, fraction, or decimal.)
x =

Answer 1

Solution,

1) x = 4

0.199 standard deviations to the left of the mean

z = -0.199

2) Given that ,

X ~ N(11, 1).

mean = = 11

variance = 2 = 1

standard deviation = = 2 = 1 = 1

z = -4.25

Using z-score formula,

x = z * +

x = -4.25 * 1 + 11

x = 6.75

3) Given that ,

X ~ N(6, 5).

mean = = 6

variance = 2 = 5

standard deviation = = 2 = 5 = 2.236

3 standard deviations to the right of the mean

z = 3.00

Using z-score formula,

x = z * +

x = 3.00 * 2.236 + 6

x = 12.71