Page 54 - Basic Statistics

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Area on the left of z value is 0.38 or P(Z <z) = 0.38, shown in Figure 3.9. Because

z lies on left of 0 then z value is negative. P (Z <z) = 0.5 - P (z <Z <0), then P(z

<Z <0) = 0.12. If applied to the symmetry properties of the normal distribution,

P(z <Z <0) = P(0 <Z <-z). From Table A.1 we get P(0 <Z <0.31) = 0.12,

subsequently obtained - z = 0.31 or z = -0.31 thus
x = (6)(-0.31) + 40

= 38.14

EXERCISES 3

1. If the random variable Z , which is standard normally distribution, use the
standard normal table Z to find:

a. P ( -2 < Z < 1,5 )
b. P ( Z< 1.97 )
c. P ( Z > 1.96 )

2. If the random variable X , which is normally distribution, has a mean 43 and
a standard deviation of 5 , find the probability:

a. P ( 40 < X < 49 )
b. P ( X < 41 )
c. P ( X > 50 )

3. Use the standard normal table Z to find the value of z, if the right side of the

area  = 0.05 ( Z0.05 )

~~* CHAPTER 3 NORMAL PROBABILITY DISTRIBUTION *~~