Page 51 - Basic Statistics

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Worked Solution: The values of the equivalent of x = 40 and x = 62 is
1
2
40 − 50
z = = -1.0
1
10
62 − 50
z = = 1.2.
2
10

thus, P ( 40 < X < 62 ) = P ( -1.0 < Z <1.2 )

Figure 3.6 P ( -1.0 < Z <1.2 )

P (-1.0 <Z <1.2) is given by the dark areas in Figure 3.6. This area can be

obtained by adding the area from -1 to 0 to the area from 0 to 1.2. Using Table
A.1, we obtain as follows

P (45< X < 62 ) = P (-1.0< Z <1.2 )

= P ( -1.0 < Z < 0 ) + P ( 0 < Z < 1.2 )

= P ( 0 < Z < 1 ) + P ( 0 < Z < 1.2 ) ( symmetry properties of Z)

= 0.3413 + 0.3849
= 0.7262

Worked Example 3.2: For a normal distribution with  = 20 and  = 5,

compute the probability that a random variable X taking a value of :

a. between 8 to 16 b. X < 12

~~* CHAPTER 3 NORMAL PROBABILITY DISTRIBUTION *~~