Answer
a. From the given normal distribution, μ= 20 and σ= 4 .
For x =20 : z = $\frac{20-20}{4}$ = 0
For x =27 : z = $\frac{27-20}{4}$ = $\frac{7}{4}$ = 1.75
$P(20 \leq x \leq 27)$ = $P( 0 \leq z \leq 1.75 )$ = 0.9599-0.5= 0.4599 approximately
b. For x =23 : z = $\frac{23-20}{4}$ = $\frac{3}{4}$ = 0.75
For x =26 : z = $\frac{26-20}{4}$ = $\frac{6}{4}$ = 1.5
$P(23 \leq x \leq 26)$ = $P( 0.75 \leq z \leq 1.5)$ =0.9332-0.7734 =0.1598 approximately
c. For x =9.5 : z = $\frac{9.5-20}{4}$ = $\frac{-10.5}{4}$ = -2.625
For x =17 : z = $\frac{17-20}{4}$ = $\frac{-3}{4}$ = -0.75
$P(9.5 \leq x \leq 17)$ = $P( -2.265\leq z \leq -0.75 )$ = 0.2266-0.0043 = 0.2223 approximately
Work Step by Step
see above
