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Charra [1.4K]
3 years ago
9

a jet flying at an altitude of 30000 ft passes over a small plane flying at 15000 feet headed in the same direction the jets fly

ing twice as fast as a small plane and 45 minutes later they are 450 miles apart find the speed of each plane
Mathematics
1 answer:
Sholpan [36]3 years ago
8 0

The jet has gained on the small plane at the rate of 10 miles per minute, so is flying 600 miles per hour faster. (There are 60 minutes in an hour.)

Since the jet is flying twice as fast as the smaller plane, the small plane's speed is the same as the difference in speed: 600 mph.

The jet's speed is double that, 1200 mph.

  • small plane: 600 mph
  • jet: 1200 mph
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z=-1.28

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a=470 -1.28*60=393.2

So the value of height that separates the bottom 10% (Fastest 10%) of data from the top 90% is 393.2.

so if the time is 393.2 or lower a boy would earn a certificate of recognition from the fitness association

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the time for this event of a population, and for this case we know the distribution for X is given by:

X \sim N(470,60)  

Where \mu=470 and \sigma=60

NOTE: For this case the fastest 10% is on the lower tail of the distribution

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.9   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.1 of the area on the left and 0.9 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.1 and P(z>-1.28)=0.9

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-1.28

And if we solve for a we got

a=470 -1.28*60=393.2

So the value of height that separates the bottom 10% (Fastest 10%) of data from the top 90% is 393.2.

so if the time is 393.2 or lower a boy would  earn a certificate of recognition from the fitness association

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