A soft drink machine is programmed to dispense an average of 400 mL per small cu

Question

A soft drink machine is programmed to dispense an average of 400 mL per small cup. Suppose the distribution of the amount of drink dispensed is normally distributed with a standard deviation of 13 mL. 2. a. What proportion of the filled small cups will contain less than 390ml? b. What proportion of the filled small cups contain between 375mL and 390ml? The maximum amount of soda the small cup can hold is 425ml; what proportion of small cups overflow? c. d. The least filed 5% of all small cups contain how much soda? DOLL

Explanation / Answer

mean =400 , s= 13

a)
P(x <390)
z= ( x - mean) / s
= ( 390 - 400) / 13
= -0.7692

P(x < 390) = P( z <-0.7692 ) = 0.2209 by using standard table

b)
P(375 < x < 390)
= p( (375 - 400)/13 < z < ( 390 -400) / 13)
= P(-1.9231 z < -0.7692

P(375 < x < 390) = P(-1.9231 < z < -0.7692) = 0.1936by using standard table

c)
P(x >425)
z= ( x - mean) / s
= ( 425 - 400) / 13
= -1.9231

P(x > 425) = P( z >-1.9231 ) = 0.0272by using standard table

d)
z value at 5% = -1.6448
z = ( x -mean) / s
-1.6448 = ( x - 400) / 13
x = 378.6176

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