(a) The support has length 920 - 720 = 200, so X has probability density
[tex]f_X(x)=\begin{cases}\frac1{200}&\text{for }720\le x\le920\\0&\text{otherwise}\end{cases}[/tex]
X has mean
[tex]E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac1{200}\int_{720}^{920}x\,\mathrm dx=\boxed{820}[/tex]
and variance
[tex]V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2[/tex]
The second moment is
[tex]E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac1{200}\int_{720}^{920}x^2\,\mathrm dx=\frac{2,027,200}3[/tex]
and so
[tex]V[X]=\dfrac{2,027,200}3-820^2=\dfrac{10,000}3[/tex]
The standard deviation is the square root of the variance, so
[tex]SD[X]=\sqrt{V[X]}=\sqrt{\dfrac{10,000}3}\approx\boxed{57.73}[/tex]
(b)
[tex]P(X<870)=\displaystyle\int_{-\infty}^{870}f_X(x)\,\mathrm dx=\frac1{200}\int_{720}^{870}\mathrm dx=\frac{870-720}{200}=\boxed{0.75}[/tex]
