Question

A random number generator picks a number from 19 to 67 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 28 is P(x = 28) =

d. The probability that the number will be between 27 and 57 is P(27 < x < 57) =

e. The probability that the number will be larger than 32 is P(x > 32) =

f. P(x > 32 | x < 59) =

g. Find the 57th percentile.

h. Find the minimum for the lower quartile.

Answer 1

Dear student, we can provide you with solution of 4 sub question at a time.

Let X be a random number selected.

According to the description of the problem, random number generator picks the number discretely, it does not choose numbers such as 1.5, 10.9, etc.

Thus, X follows a discrete uniform distribution of range [ 19 , 67 ].

here n = 67 - 19 + 1 = 49

a) The mean of the distribution is

b) standard deviation of the distribution is

c) Probability that the number will be exactly 28 is

d) The probability that the number will be between 27 and 57 ( there is a total of (57-27 -1 =29) number between 27 and 57)is

e) the probability that the number will be larger than 32 is