Answer:
The standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
Step-by-step explanation:
Let the random variable <em>X</em> denote the amount of coffee dispensed by the machine.
It is provided that the random variable, <em>X</em> is normally distributed with mean, <em>μ</em> = 105 ml/cup and standard deviation, <em>σ</em>.
It is also provided that a sign on the machine indicates that each cup contains 100 ml of coffee.
And 10% of the cups contain less than the amount stated on the sign.
To compute the probabilities of a normally distributed random variable, first convert the raw score to a <em>z</em>-score,
This implies that:
P (X < 100) = 0.10
⇒ P (Z < z) = 0.10
The value of <em>z</em> for the above probability is, <em>z</em> = -1.28.
*Use a <em>z</em>-table
Compute the value of standard deviation as follows:
Thus, the standard deviation of the amount of coffee dispensed per cup in ml is 3.91.