There are 12 such shapes. One can start with two squares, adding squares around the edge and rejecting shapes that have been previously seen. Repeating until you have 5 squares results in 12 distinct shapes.
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2 shapes are possible with 3 squares: L, I
5 shapes are possible with 4 squares: L, I, N, T, O
The sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.
p-hat proportion:
In this proportion, "p" denotes the probability of a certain event occurring or a certain parameter being true for a certain population, but when a population is large, it may be impractical or impossible to measure it directly. So, we have used the proportion for that cases.
The general form for calculating p-hat proportion is,
where
x is the number of successes in the sample, and
y is the size of the sample.
Given,
In a random sample of 200 engineers, 137 have a master's degree.
Here we need to find the the sample proportion, p-hat, of engineers who have master's degrees
According to the question,
x = 137 (number of successes in the sample)
and y = 200 (size of the sample)
Now apply the value on the formula then we get,
So, the value of p-hat is
The results are usually reported as a percentage, which in this case would be
=> 0.685 x 100 = 68.5%
Therefore, the sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.
To know more about p-hat proportion here
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