An empty shipping box box weighs 250 grams. The box is filled with T shirts weighs 132.5 grams. The equation W=250+132.5T repres
1 answer:
You might be interested in
Answer:
a) 0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.
b) 0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.
Step-by-step explanation:
Binomial 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.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
To use the Poisson approximation for the binomial, we have that:
1 in every 2500 automobiles produced has a particular manufacturing defect.
This means that
a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 7000 cars.
This is when
. So
0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.
(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p.
Using the approximation:
. So
0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.
The increasing and decreasing intervals are marked on the graph and attached below.
The red arrow mark shows the part where graph is decreasing
The green arrow mark shows the part where graph is increasing
There is no end point or starting point for the graph
The graph starts decreasing at -∞ and it decreases till it reaches -2.5
Also the graph start decreasing at 0 and goes to +∞
So we have two decreasing intervals
(-∞ , -2.5) U (0, ∞)
The graph starts increasing at -2.5 and it increases till it reaches 0
So increasing interval is
(-2.5, 0)
