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 X denote the amount of coffee dispensed by the machine.
It is provided that the random variable, X is normally distributed with mean, μ = 105 ml/cup and standard deviation, σ.
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 z-score,
[tex]z=\frac{X-\mu}{\sigma}[/tex]
This implies that:
P (X < 100) = 0.10
⇒ P (Z < z) = 0.10
The value of z for the above probability is, z = -1.28.
*Use a z-table
Compute the value of standard deviation as follows:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]-1.28=\frac{100-105}{\sigma}[/tex]
[tex]\sigma=\frac{-5}{-1.28}[/tex]
[tex]=3.90625\\\\\approx 3.91[/tex]
Thus, the standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
