Molly is converting 2 yards to millimeters. Will the number of millimeters be fewer than or greater than 2?
1 answer:
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Answer:
So the value of height that separates the bottom 45% of data from the top 55% is 1022.532.
Step-by-step explanation:
1) 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".
2) Solution to the problem
Let X the random variable that represent the consumption levels of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(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 0.45 of the area on the left and 0.55 of the area on the right it's z=-0.26. On this case P(Z<-0.126)=0.45 and P(z>-0.126)=0.55
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 45% of data from the top 55% is 1022.532.
Answer:
Option B is correct.
67.5 degree
Step-by-step explanation:
To find the angle between the hands of a clock.
Given that:
Hands of a clock at 5 : 15.
We know that:
A clock is a circle and it always contains 360 degree.
Since, there are 60 minutes on a clock.
so, each minute is 6 degree.
The minutes hand on the clock will point at 15 minute,
then, its position on the clock is:
Also, there are 12 hours on the clock
⇒Each hour is 30 degree.
Now, can calculate where the hour hand at 5:00 clock.
⇒
Since, the hours hand is between 5 and 6 and we are looking for 5:15 then :
15 minutes is equal to of an hour
⇒
Then the angle between two hands of clock:
⇒
Therefore, the angle between the hands of a clock at 5: 15 is: 67.5 degree.