A random variable follows the continuous uniform distribution between 50 and 80.

Question

A random variable follows the continuous uniform distribution between 50 and 80. Calculate the following quantities for the distribution. a) P(x > 59) b) P(x> 60) c) P(x> 76) d) P(x 74) e) What are the mean and standard deviation of this distribution? a) P(x > 59)- (Type an integer or decimal rounded to three decimal places as needed.) b) P(x-60) (Type an integer or decimal rounded to three decimal places as needed.) c) Px76) (Type an integer or decimal rounded to three decimal places as needed.) d) Px 74)- (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

Explanation / Answer

For uniform distribution it is given that a=50 and b=80

a) P(x>59)=(b-x)/(b-a) =(80-59)/(80-50)=21/30=0.7

b) P(c>60)=(80-60)/(80-50)=2/3 or 0.667

c) P(x>76)=(80-76)/(80-50)=4/30

d) P(x=74)=0 (because point probability is 0 for continuous distributions)

e) MEAN is (a+b)/2 =(50+80)/2=65

standard deviation is square root of variance. Variance is given by (b-a)^2 /12 or (30)^2/12 =75

thus SD is sqrt(75)= 8.66

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