#### Answer

a. From the given normal distribution, μ= 46 and σ= 4.
For x =40 : z = $\frac{40-46}{4}$ = -1.5
$P(x \gt 40)$ = $P(z \gt -1.5 )$ = .9332 approximately.
b. For x =50 : z = $\frac{50-46}{4}$ = 1
For x =57: z = $\frac{57-46}{4}$ = 2.75
$P(50 \leq x \leq 57)$ = $P(1\leq z \leq 2.75)$ = 0.997-0.8413 = .1557 approximately.

#### Work Step by Step

see above