Question

A random number generator picks a number from 8 to 75 in a uniform manner. Round answers to 4 decimal places when possible. a. The mean of this distribution is b. The standard deviation is C. The probability that the number will be exactly 15 is P(x = 15) - O d. The probability that the number will be between 12 and 33 is P(12 < x < 33) = e. The probability that the number will be larger than 22 is P(x > 22) = f. P(x > 24 | X < 26) = g. Find the 64th percentile. h. Find the minimum for the lower quartile.

Answer 1

a) Mean = (a + b)/2 = (8 + 75)/2 = 41.5

b) Standard deviation = (b - a)/√12 = (75 - 8)/√12 = 19.3412

c) P(x = 15) = 0

d) P(12< X < 33) = (x2 - x1)/(b - a) =   

= (33 - 12)/(75 - 8) = 0.3134   

e) P(X > 22) = (b - x)/(b - a) =   

= (75 - 22)/(75 - 8) = 0.7910

f) P(24< X < 26) = (x2 - x1)/(b - a) =   

= (26 - 24)/(75 - 8) =    0.0299

P(X < 26) = (x - a)/(b - a) =   

= (26 - 8)/(75 - 8) =    0.2687

P(x > 24 | x < 26) = P(24 < x < 26)/ P(X < 26)

= 0.0299/0.2687

= 0.1113

g) Let the number be x at 64 percentile

= (x -8)/(75 - 8) = 0.64  

x = 50.88

h) Let the number be x  

= (x -8)/(75 - 8) = 0.25  

x = 24.75