I need help with finding the limit for problem #1. I've already solved 2-4 I just don't get the first one.
1 answer:
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Answer:
a) There is a 74.22% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
b) There is a 1-0.0548 = 0.9452 = 94.52% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.
c) There is a 68.74% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
.
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 3.3 minutes. This means that .
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?
We are working with a sample mean of 37 jets. So we have that:
Total time of 320 minutes for 37 jets, so
This probability is the pvalue of Z when . So
has a pvalue of 0.7422. This means that there is a 74.22% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?
Total time of 275 minutes for 37 jets, so
This probability is subtracted by the pvalue of Z when
has a pvalue of 0.0548.
There is a 1-0.0548 = 0.9452 = 94.52% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.
(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?
Total time of 320 minutes for 37 jets, so
Total time of 275 minutes for 37 jets, so
This probability is the pvalue of Z when subtracted by the pvalue of Z when
.
So:
From a), we have that for , we have
, that has a pvalue of 0.7422.
From b), we have that for , we have
, that has a pvalue of 0.0548.
So there is a 0.7422 - 0.0548 = 0.6874 = 68.74% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes.
To find the missing angle first we need to fill in the other angles.
If we look at the 128 its on a straight line that is separated by another straight line so to get the angle on the other side of the line we need to subtract 128 from 180 which is 52.
The same goes for 160 so 180-160 = 20
And again the same for 60 so 180-60 = 120
So now that we have 2 out of 3 angles in the triangle we can figure out the final one by subtracting 120 and 20 from 180 (because theres 180 degrees in a triangle) which equals 40
Now if we look at the 40 degrees the other side is its opposite which makes it the same degree, and now we once again have 2 out of the 3 angles in a triangle so go to the triangle with 52 degrees and 40 degrees and subtract them from 180 which would be 88 degrees.
Now we subtract 88 from 180 to get the missing angle that we need (because its on another straight line thats been separated by another straight line) which equals 92
So the answer to your question is 92 degrees
If we look at the 128 its on a straight line that is separated by another straight line so to get the angle on the other side of the line we need to subtract 128 from 180 which is 52.
The same goes for 160 so 180-160 = 20
And again the same for 60 so 180-60 = 120
So now that we have 2 out of 3 angles in the triangle we can figure out the final one by subtracting 120 and 20 from 180 (because theres 180 degrees in a triangle) which equals 40
Now if we look at the 40 degrees the other side is its opposite which makes it the same degree, and now we once again have 2 out of the 3 angles in a triangle so go to the triangle with 52 degrees and 40 degrees and subtract them from 180 which would be 88 degrees.
Now we subtract 88 from 180 to get the missing angle that we need (because its on another straight line thats been separated by another straight line) which equals 92
So the answer to your question is 92 degrees
Answer:
120 different color combinations are possible.
Step-by-step explanation:
The order in which the color are chosen is not important(blue, green and red is the same outcome as red, blue, green), which means that the combinations formula is used to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
3 colors from a set of 10, so:
120 different color combinations are possible.