Page 50 - Basic Statistics

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1.74. First find the value of z is equal to 1.7 in the leftmost column, and then

view along the raw until the column below 0.04, there we read 0.4591. Thus
P(0 <Z <1.74) = 0.4591.

Figure 3.5 Probability of Z between 0 to z
P ( 0 < Z < z )

Sometimes, we are asked to find the value of z for a given probability

value and the z value is between the values listed in Table A.1. For simplicity,

we will take the value of z in the table which its probability value closest to
probability value known. However, if the probability is known that falls right in

the middle between the two tables, then the value of z we get an average of the

two values of z matching both values in the table. For example, to find the value

of z that generates probability for 0.2975, which lies between 0.2967 and 0.2995

in Table A.1, we will take z = 0.83, since 0.2975 is closer to 0.2967. But for a
probability at 0.2981, which falls right in the middle of 0.2967 and 0.2995, we

will take z = 0.835.

Worked Example 3.1: For a normal distribution with  = 50 and  = 10,

compute the probability that X taking a value between 40 and 62.

~~* CHAPTER 3 NORMAL PROBABILITY DISTRIBUTION *~~