A random variable follows the continuous uniform distribution between 65 and 110

Question

A random variable follows the continuous uniform distribution between 65 and 110. Calculate the following quantities for the dist a) P/x> 66) b) P(x> 75) c) P(x> 101) d) P/x 84) e) What are the mean and standard deviation of this distribution? a) Px> 66) (Type an integer or decimal rounded to three decimal places as needed.) b) P(x > 75) Type an integer or decimal rounded to three decimal places as needed.) ) Px 101)- (Type an integer or decimal rounded to three decimal places as needed) d) P/x 84) (Type an integer or decimal rounded to three decimal places as needed.) e) The mean of this distribution is Type an integer or a decimal) The standard deviation of this distribution is Type an integer or decimal rounded to two decimal places as needed)

Explanation / Answer

e ) Mean µ =(a + b)/2
=(65 + 110)/2
=175/2

Variance 2 =
(b - a)^2/12
=
(110 - 65)^2/12
=
(45)^2/12
=2025/12
Variance 2 = 168.75

SD= 12.990

D)  Find P value using a, b & x values
f(x) =1/(b - a)
=1/(110 - 65)
=1/45
P = 0.0222

Formula For (1,2,3)

P(X) = (b – c )/ (b – a)

P(X>66) = (110 -66)/(110-65) =0.9778

P(X>75) = (110 -75)/(110-65) =0.7778

P(X>101) = (110 -101)/(110-65) =0.200

thanks :)

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