Question

7. Starbucks Cappuccino times follow a Continuous or Uniform distribution:

The time required to make Cappuccino using whole milk is uniformly distributed between 25 and 35 seconds.

Estimate the Population mean and standard deviation of Cappuccino times at Starbucks.

Estimate the Probability that the Cappuccino will take less than 30 seconds. Estimate the Probability that the prepeartion time will be less than 35 seconds.

Answer 1

Solution :

Given that,

a = 25

b = 35

mean = (a + b) / 2

= ( 25 + 35 ) / 2

= 60 / 2

= 30

mean = 30

standard deviation =  (b - a)2/12  

= ( 35 - 25 )2 / 12

= 100 / 12

= 8.33

= 2.89

standard deviation = 2.89

P(x < 30 ) = (30 - 25) / (35 - 25)

= 5 / 10

= 0.5

Probability = 0.5

P(x < 35 ) = (35 - 25) / (35 - 25)

= 10 / 10

= 1

Probability = 1