hey, do any of you guys know how to plot functions on a graph. You know like f(X) and g(X)? I find it really hard and also do yo
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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.
Answer:
Step-by-step explanation:
the equation for finding the slope of a line when given two points is , aka the change in y over the change in x.
pick one of your coordinate pairs to be and
. it doesn't matter which coordinate pair you choose as long as you keep them as
and
. the remaining coordinate pair will be
and
.
for this example, i'll use (2, 10) for and
and (6, 7) for
and
.
<em>**before i begin, i just want to note that you can do these next four steps in any order that you want. i personally prefer to plug in my y-values first and then my x-values, but you can choose to instead plug in the values of each coordinate pair (like starting by plugging in the coordinate pair (2, 10) with 10 for </em> and 2 for
<em>). it's up to you. i'm going to explain the steps by plugging in my y-values first and then my x-values because that's the way i normally do it.</em>
<em />
first, start by plugging in the y-value from the coordinate pair of your choosing in for . since i chose (2, 10) for
and
, i'll plug in 10 for
.
⇒
then plug in the remaining coordinate pair's y-value in for . since the coordinate pair that's left is (6, 7), i will plug in 7 for
.
⇒
now i'm going to plug in the x-values. i chose (2, 10) to plug in for and
, so now i'll plug in 2 for
.
⇒
and all that's left to plug in is the x-value from (6, 7), so i will plug that in for .
⇒
after plugging in all the values, you have .
subtract 10 - 7 as well as 2 - 6.
⇒
cannot be simplified, therefore the slope of the line is
or
.
i hope this helps! have a lovely day <3