Question

Find the probabilities for each, using the standard normal distribution table.

Include a sketch of the graph for each case.

a) ?? ?h? ???h? ?? ? = −1.28

b) ???h????????=0.72

c) ??????? ? = 0.46 ??? ? = −1.35

Answer 1

Solution(a)
We need to calculate the probability of right of Z = -1.28
i.e. P(Z>-1.28) = ?
From Z table we found a p-value
P(Z>-1.28) = 1 - P(Z<=-1.28) = 1 - 0.1003 = 0.8997
So there is 89.97% area to the right of Z = -1.28
Solution(b)
We need to calculate the probability of left of Z = 0.72
i.e. P(Z<0.72) = ?
From Z table we found a p-value
P(Z<0.72) = 0.7642
So there is 76.42% area to the left of Z = 0.72
Solution(c)
P(-1.35<Z<0.46) = P(Z<0.46) - P(Z<-1.35)
From Z table we found p-value
P(-1.35<Z<0.46) = P(Z<0.46) - P(Z<-1.35) = 0.6772 - 0.0885 = 0.5887
So there is 58.87% area between ? = 0.46 ??? ? = −1.35