Question

Q6.     

By using the stander normal curve, find the following.

i.P ( -1.5 < z < -1)

ii.P ( z = 3)

iii.P ( -2 < z < 3)

iv.P(z < z₀ ) = 0.125

v.Probability of z>-1 or z<2

Answer 1

Here, we would be using the cumulative standard normal tables to compute the given probabilities.

a) P( -1.5 < Z < -1 )

= P(Z < -1 ) - P(Z < -1.5)

Getting these from the standard normal tables, we get:

= 0.1587 - 0.0668

= 0.0919

Therefore 0.0919 is the required probability here.

(ii) As the normal distribution is a continuous distribution, the probability of Z taking an exact value is always 0

Therefore 0 is the required probability here.

(iii) P( -2 < Z < 3 )

= P(Z < 3) - P(Z < -2 )

Getting it from the standard normal tables, we get:

= 0.9987 - 0.0228

= 0.9759

Therefore 0.9759 is the required probability here.

(iv) From the standard normal tables we get:

P(Z < -1.15) = 0.125

Therefore the value of Z₀ here is -1.15

(v) P(Z > -1 ) + P(Z < 2)

Note that this is always true, because when Z > -1 Then it is true and when Z < -1, then Z has to be less than 2 as well and therefore,

P(Z > -1 ) + P(Z < 2) = 1

Therefore 1 is the required probability here.