A random number generator picks a number from 10 to 42 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 12 is P(x = 12) = d. The probability that the number will be between 16 and 19 is P(16 < x < 19) = e. The probability that the number will be larger than 16 is P(x > 16) = f. P(x > 16 | x < 27) = g. Find the 69th percentile. h. Find the maximum for the lower quartile.

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A random number generator picks a number from 10 to 42 in a uniform manner. Round answers to 4 decimal places when possible. (a-h)

A random number generator picks a number from 10 to 42 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 12 is P(x = 12) =
%3D
d. The probability that the number will be between 16 and 19 is P(16 < x < 19) =
e. The probability that the number will be larger than 16 is P(x &gt 16) =
f. P(x > 16 | x < 27) =
%3D
g. Find the 69th percentile.
h. Find the maximum for the lower quartile.
Transcribed Image Text:A random number generator picks a number from 10 to 42 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 12 is P(x = 12) = %3D d. The probability that the number will be between 16 and 19 is P(16 < x < 19) = e. The probability that the number will be larger than 16 is P(x &gt 16) = f. P(x > 16 | x < 27) = %3D g. Find the 69th percentile. h. Find the maximum for the lower quartile.
Expert Solution
Formulae :-

Uniform Distribution :-

If X follows uniform distribution over interval ( a, b ) then probability distribution function ( PDF ) of X is , 

f(x) = 1b - a    ,  a  x  b0Otherwise  

Mean = a + b 2

Standard deviation = (b-a)212

The cumulative distribution function (CDF) of X is ,

P( X x ) = x -ab - a  ,  axb

 

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