The distance of planet Mercury from the Sun is approximately 5.8 ⋅ 10^7 kilometers, and the distance of Earth from the Sun is 1.
2 answers:
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The question is incomplete. Here is the complete qeustion.
In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained: 0.10 0.13 0.16 0.15 0.14 0.008 0.15
(a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars.
(b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a), can we safely conclude that this requirement is being met?
Answer: (a) 0.089 ≤ μ ≤ 0.171
(b) No
Step-by-step explanation:
(a) To determine the confidence interval, first calculate the mean (X) and standard deviation (s) of the sample
X =
X = 0.13
s =
s = 0.029
The degrees of freedom is
N - 1 = 7 - 1 = 6
And since the confidence is of 99%:
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
The t-test statistics for is 3.707
(Value found in the t-distribution table)
Now, calculate Error:
E = .
E = 3.707.
E = 0.041
The interval will be:
0.13 - 0.041 ≤ μ ≤ 0.13+0.041
0.089 ≤ μ ≤ 0.171
(b) No, because according to the interval, the nitrode-oxide emissions range from 0.089 to 0.171, which is greater than required by EPA.
Answer:
Q1) The student has a 0.01% probability of passing the test.
Q2) She has a 99.91% probability of passing in the test.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he gets it correct, or he gets it wrong. So we solve this problem using the binomial probability distribution.
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 combinatios of x objects from a set of n elements, given by the following formula.
And is the probability of X happening.
For this problem, we have that:
Question 1.
There are 50 questions, so .
The student is going to guess each question, so he has a probability of getting it right.
He needs to get at least 25 question right.
So we need to find .
Using a binomial probability calculator, with and
we get that
.
This means that the student has a 0.01% probability of passing the test.
Question 2.
Now, we need to find with
. So
She has a 99.91% probability of passing in the test.