Assume the time required to pass through security at a particular airport follow

Question

Assume the time required to pass through security at a particular airport follows the continuous uniform distribution with a minimum time of 5 minutes and maximum time of 29 minutes. Complete parts (a) through (f) below. a) Calculate the value of fx). fx)(Type an integer or decimal rounded to three decimal places as needed) b) What are the mean and standard deviation for this distribution? The mean of this distribution is minutes Type an integer or a decimal.) The standard deviation of this distribution is minutes. (Type an integer or decimal rounded to two decimal places as needed.)

Explanation / Answer

a=5 and b=29 for uniform distribution

a) f(x)=x/(b-a)=x/(29-5)=x/24

b) mean is (a+b)/2=(29+5)/2=17

standard deviation is (b-a)/sqrt(12)=24/sqrt(12)=6.9282

c) P(x<23)=(23-5)/(29-5)=0.75

d) P(x>21)=(29-21)/(29-5)=0.3333

e) P(10<x<13)=(13-10)/(29-5)=0.125

f) for 0.75 =(x-5)/(29-5) we get x=23

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