- Normal area calculations. Z = Standard NOrmal

a. Determine P(-1.5 < Z < 1.5) (the area beneath the standard normal curve between Z=-1.5 and Z=1.5).

Probability:

b. Find the P(0.8 < Z < 1.7).

Probability:

c. Find the value of z such that P(Z < z)=0.25.

Probability:

d. Your answer to part (c) above is Q₁for a standard normal variable, since the relative frequency to the left of the value is 0.25. What are Q₂(the median, Find the value of z such that P(Z < z)=0.50) and Q₃(Find the value of z such that P(Z < z)=0.75)of a standard normal variable?

Q₂:

Q₃:

e. Suppose X has a normal distribution with mean 10.0 and standard deviation 5.0.

What is the P(2.0 < X < 14.0)?

P(2.0 < X < 14.0)=

f. Suppose X has a normal distribution with mean 10.0 and standard deviation 2.0. What is the P(2.0 < X < 14.0)?

P(2.0 < X < 14.0)=