Question

The time it takes for a data collection operator to fill out an electronic form for a database is uniformly distributed between 7.5 and 14 minutes.

a. What is the mean time it takes to process an electronic form?

b. What is the standard deviation of the time it takes to process an electronic form?

c. What is the probability that it takes more than 10 minutes to fill out a form?

d. What is the probability it takes between 8 and 10 minutes to process an electronic form?

e. Given that it took more than 10 minutes to fill out the form, what is the probability it took less than 11 minutes to fill out the form?

f. What is the probability it takes an operator more than 15 minutes to fill out the form?

Answer 1

here for uniform distribution parameter a =7.5 and b=14

a)

mean μ =

(a+b)/2 =

10.75

b)

standard deviation σ=(b-a)/√12=

1.8764

c)

probability =

P(X>10)=

1-P(X<10)=

1-(10-7.5)/(14-7.5)=

0.6154

d)

probability =

P(8<X<10)=

(10-8)/(14-7.5)=

0.3077

e)

P(X<11 |X>10 ) =P(10<X<11)/P(X>10)=((11-10)/(14-7.5))/(14-10)/(14-7.5))=0.25

f) probability it takes an operator more than 15 minutes to fill out the form =0

(since 15 minute is outside the domain of distribution)