Answer
a) P( 1.8 < x < 2.2)= 0.5762
b) P( 2.1 < x < 2.7) = 0.342
c) P( x > 2.3) = 0.1151
Work Step by Step
PART A
i) Find corresponding z scores using z = $\frac{x - \mu }{\sigma}$
z = $\frac{1.8 - 2}{0.25} = -0.8$
z = $\frac{2.2 - 2}{0.25} = 0.8$
ii) P (-0.8 < z < 0.8)
= P(z < 0.8) - P(z < -0.8)
= 0.7881 - 0.2119
=0.5762
PART B
i) Find corresponding z scores
$P(2.1 < x < 2.7)$ = $P(\frac{2.1 - 2}{0.25} < z < \frac{2.7 - 2}{0.25})$ = $P(0.4 < z < 2.8)$
ii) Evaluate $P(0.4 < z < 2.8)$
= P(z < 2.8) - P(z < 0.4)
= 0.9974 - 0.6554
= 0.342
PART C
i) Find corresponding z score
$P(x > 2.3) = P(z > \frac{2.3 - 2}{0.25}) = P(z > 1.2)$
ii) Evaluate $P(z > 1.2)$
= 1 - $P(z <1.2)$
= 1- 0.8849
= 0.1151
