A machine dispenses a carbonated drink into bottlesbefore these are sealed. while the machine is supposed to dispense 250 ml of drink into each bottle, the actual amount of drink dispense 250 ml of drink into each bottle, the actual amount of drink dispensed is normally distributed with a mean of 245 ml and a standard deviation of 6ml find the probability that a bottle randomly selected from the product output
a. more than 255ml of drink
b. less than 235 ml of drink
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Given : A machine dispenses a carbonated drink into bottles
Actual amount of drink dispensed is normally distributed with a mean of 245 ml and a standard deviation of 6ml
To Find : the probability that a bottle randomly selected from the product output
a. more than 255ml of drink
b. less than 235 ml of drink
Solution:
Mean = 245
SD = 6
Z score = ( Value - Mean)/SD
more than 255ml of drink
Z score for 255
=> Z = (255 - 245)/6 = 10/6 = 5/3 = 1.667
=> 0.952 bottles are upto 255 ml
more than 255ml of drink = 1 - 0.952
= 0.048
probability that a bottle randomly selected from the product output
a. more than 255ml of drink = 0.048
less than 235 ml of drink
Z score = (235 - 245)/6 = -10/6 = -5/3 = -1.667
=> 0.048 bottles are upto 235 ml
probability that a bottle randomly selected from the product output
Less than 235 ml of drink = 0.048
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