Solve the following problem. Choose the correct answer. Ink, Inc., offers pencils at $1.10 per dozen, with a 1.5% discount for p
urchases of more than 12 dozen. If Jerry buys 19 dozen for his club, how much does he pay? Jerry pays $ total.
2 answers:
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Given:
The point is (-12,-8).
Rule of transformation is .
To find:
The coordinates of image after transformation.
Solution:
According to the rule of transformation , first the point is dilated by factor
with origin as center of dilation after that it was rotated 270 degrees anticlockwise.
If a point is dilated by factor with origin as center of dilation, then
If a point is rotated 270 degrees anticlockwise, then
Therefore, the coordinates of image after transformation are (-2,3).
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.