Step 1a

Finding the Probability density function

Explanation:

For X∼ U(a,b)

f(x) = \$1/(b-a)\$ a<x<b

Given X∼ U(200,250)

f(x) = \$1/(250-200)\$ 200<x<250

f(x) = \$1/50\$ 200<x<250

Step 1b

Finding P (X > 230)

Explanation:

P (X > 230) = \$\int_230^\infty f(x) dx\$

P (X > 230) = \$\int_230^250 1/50 dx\$

where f(x) = \$1/50\$

P (X > 230) = \$1/50\$ \$ (x)_230^250\$

P (X > 230) = \$(250-230)/50 = 20/50\$

P (X > 230) = 0.4

Step 1c

Calculate the Mean,median,standard deviation.

Explanation:

Given X∼ U(200,250)

a = 200,b = 250

mean = median = \$(a+b)/2\$

mean = median = \$(200+250)/2\$

mean = median = \$450/2\$

mean = median = 225

Standard deviation = \$\sqrt((b-a)^2/12)\$

S.D = \$\sqrt((250-200)^2/12)\$

S.D = \$\sqrt(50^2/12)\$

S.D = \$\sqrt(2500/12)\$

S.D = \$50/\sqrt12\$

S.D = \$50/3.464\$

S.D = 14.434