A vending machine dispenses coffee into a twelve ounce cup he amount of coffee dispensed into the cup is normally distributed wi
1 answer:
Answer:
this mean amount of coffee to be dispensed would be 11.99, approximately 12
Step-by-step explanation:
first of all we have this information available to answer this question.
standard deviation σ = 0.006 ounces
prob(x > 12) = 0.04
we use this formular to find the mean
z = x - μ/σ
the value of the z score at 4% is equal to 1.7507
such that
we cross multiply from this stage
1.7507*0.006 = 12-μ
0.0105042 = 12-μ
μ = 12 - 0.0105042
herefore, the mean amount μ = 11.99 this can be approximated to 12
You might be interested in
Answer:
a) 0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.
b) 0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.
c) 0.064 = 6.4% probability that 7 of them are discovered.
Step-by-step explanation:
For itens a and b, we use conditional probability.
For item c, we use the binomial distribution along with the conditional probability.
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
a) If it has an emergency locator, what is the probability that it will not be discovered?
Event A: Has an emergency locator
Event B: Not located.
Probability of having an emergency locator:
66% of 72%(Are discovered).
20% of 100 - 72 = 28%(not discovered). So
Probability of having an emergency locator and not being discovered:
20% of 28%. So
Probability:
0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.
b) If it does not have an emergency locator, what is the probability that it will be discovered?
Probability of not having an emergency locator:
0.5312 of having. So
Probability of not having an emergency locator and being discovered:
34% of 72%. So
Probability:
0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.
c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?
p is the probability of being discovered with the emergency recorder:
0.5312 probability of having the emergency recorder.
Probability of having the emergency recorder and being located:
66% of 72%. So
Probability of being discovered, given that it has the emergency recorder:
This question asks for P(X = 7) when . So
0.064 = 6.4% probability that 7 of them are discovered.