Task 7.1 The normal probabilistic distribution (54 points)

Instructions:

After reading and analyzing the material presented in sections 6-1, 6-2 and 6-3, perform the exercises for this activity, which will evaluate your learning about the basic concepts of normal probability distribution. You must present the necessary processes to support the response of the exercises. (2 points each exercise).

1) Consider a standard normal random variable with = 0 and a standard deviation = 1. Use table 3 to find the following probabilities:

a) P (Z <2.93)

b) P (Z> 1.36)

c) P (-2.73

d) P (Z <-1.97)

e) P (Z <-1.67)

2) Find these probabilities associated with the standard normal random variable Z:

a) P (Z> 2.54)

b) P (-3.3

c) P (Z <1.84)

d) P (Z> 2.85)

e) P (Z> 3.16)

3) Calculate the area under the standard normal curve to the left of these values:

a) Z = 1.87

b) Z = 0.61

c) Z = 1.45

d) Z = 2.72

4) Calculate the area under the curve between these values:

a) Z = -2.7 and Z = 2.7

b) Z = -3.1 and Z = 3.1

c) Z = -1.95 and Z = 1.95

d) Z = -2.26 and Z = 2.26

e) Z = -3.30 and Z = 3.30

5) Calculate the area under the curve to the left of these values:

a) Z = -.87

b) Z = 2.55

c) Z = 2.86

d) Z = 3.23

e) Z = -2.58

6) A standard normal random variable has = 0 and a standard deviation = 1. Use table 3 to find the probability less than -2.51.

7) A standard normal random variable has = 0 and a standard deviation = 1. Use table 3 to find the probability greater than 3.48.

8) A standard normal random variable has = 0 and a standard deviation = 1. Use table 3 to find the probability between -1.00 and 3.40.