Question

(1 point) Suppose a random variable ? is best described by a uniform probability distribution with range 1 to 4. Find the value of ?a that makes the following probability statements true.

(a)  ?(?≤?)=0.26
?=

(b)  ?(?<?)=0.95
?=

(c)  ?(?≥?)=0.65
?=

(d)  ?(?>?)=0.25
?=

(e)  ?(1.49≤?≤?)=0.06

a=

Answer 1

a) P(x < a) = 0.26

Or, (a - 1)/(4 - 1) = 0.26

Or, (a - 1)/3 = 0.26

Or, a = 0.26 * 3 + 1

Or, a = 1.78

b) P(x < a) = 0.95

Or, (a - 1)/(4 - 1) = 0.95

Or, (a - 1)/3 = 0.95

Or, a = 0.95 * 3 + 1

Or, a = 3.85

c) P(x > a) = 0.65

Or, (4 - a)/(4 - 1) = 0.65

Or, (4 - a)/3 = 0.65

Or, a = 4 - 3 * 0.65

Or, a = 2.05

d) P(x > a) = 0.25

Or, (4 - a)/(4 - 1) = 0.25

Or, (4 - a)/3 = 0.25

Or, a = 4 - 3 * 0.25

Or, a = 3.25

e) P(1.49 < x < a) = 0.06

Or, (a - 1.49)/(4 - 1) = 0.06

Or, (a - 1.49)/3 = 0.06

Or, a = 0.06 * 3 + 1.49

Or, a = 1.67