A machine is used to fill soda bottles. The amount of soda dispensed into each b

Question

A machine is used to fill soda bottles. The amount of soda dispensed into each bottle varies slightly. The amount of soda dispensed into the bottles is normally distributed with a mean of 590 mililiters and a standard deviation of 2.6 milliliters. What is the probability that the amount of soda in the bottle is between 593 and 596 milliliters?

a. 0.4896

b. 0.1147

c. 0.8645

d. 0.3749

e. 0.6147

What is the probability that the amount of soda in the bottle is above 596.5 milliliters?

a. 0.9938

b. 0.5062

c. 0.0062

d. 0.5000

e. 0.4938

Explanation / Answer

Solution:

From the given information Mean = 590
Standard deviation = 2.6
P(593 < X < 596 ) = P ( 593590/2.6 < X/ < 596590/2.6)
= P ( 1.15 < Z < 2.31 )
= P ( Z < 2.31 )P (Z < 1.15 )
= 0.9896 - 0.8749
= 0.1147
So, option b. 0.1147 is the answer

......................................

Given information Mean = 590
Standard deviation = 2.6

P(X > 596.5 ) = P( X/ > 596.5590/2.6)
= P (Z > 2.5 )
= 1P (Z < 2.5 )
= 10.9938 = 0.0062
So here option c. 0.0062 is the answer

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