Question

A random number generator picks a number from 18 to 64 in a uniform manner. Round answers to 4 decimal places when possible.

The mean of the distribution is:

The standard deviation is:

The probability that the number will be exactly 20 is P(x = 20) =

The probability that the number will be between 24 and 26 is P(24 < x < 26) =

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

P(x > 19 | x < 51) =

Find the 79th percentile.

Find the minimum for the upper quartile.

Answer 1

X ~ U(18,64)

X follows Uniform distribution,

The pdf is given by,

The mean of the distribution is

= 82/2 = 41

The standard deviation is

= 13.2791

The probability that number will be exactly 20

= P(X = 20) = 20/46 = 10/23 = 0.4348

The probability that the number will be between 24 and 26 is P(24 < x < 26)

= (26-24)/(46) = 2/46 = 1/23 = 0.0435

The probability that the number will be larger than 32 is P(x > 32) = (64-32)/46 = 32/46 = 16/23 = 0.6956

P(x > 19 | x < 51) = P(19<X < 51) / P(X<51) = (51-19) / (51-18) = 32/33 = 0.9697

79th percentile = P(X<k) = (k-18)/46 = 0.79,

k = 46*0.79+18 = 54.34 (ans)

upper quartile,

k = 46*0.75+18 = 34.5+18 = 52.5

minimum for upper quartile = 52.5 (ans)

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