Question

A random number generator picks a number from 15 to 39 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 34 is P(x = 34) =____ d. The probability that the number will be between 17 and 24 is P(17 < x < 24) =_____ e. The probability that the number will be larger than 23 is P(x > 23) =_____ f. P(x > 24 | x < 30) =____ g. Find the 48th percentile._____ h. Find the minimum for the upper quartile._____

*answers accurate to at least 4 decimal places.

Answer 1

X ~ U (15 , 39)

a) mean = (15 + 39) / 2 = 27

b) standard deviation = (39 - 15) / sqrt(12) = 6.9282

c) total numbers = 39 - 15 + 1 = 25

P(X = 34) = 1 / 25 = 0.04

d) P(17 < X < 24) = (24 - 17 - 1) / 25 = 0.24

e) P(X > 23) = (39 - 23) / 25 = 0.64

f) P(x > 24 | x < 30) = P(24 < x < 30) / P(x < 30) = [(30 - 24 - 1)/25] / [(30 - 15 + 1) / 25] = 5 / 16 = 0.3125

g) P(X < x) = 0.48

or, (x - 15 + 1) / 25 = 0.48

or, x = 26

h) P(X < x) = 0.75

or, (x - 15 + 1) / 25 = 0.75

or, x = 32.75