The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the face value of
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Answer:
(a) The mean or expected value of <em>X </em>is 2.2.
(b) The standard deviation of <em>X</em> is 1.3.
Step-by-step explanation:
Let <em>X</em> = number of times the traffic light is red when a commuter passes through the traffic lights.
The probability distribution of <em>X</em> id provided.
The formula to compute the mean or expected value of <em>X </em>is:
The formula to compute the standard deviation of <em>X </em>is:
The formula of E (X²) is:
(a)
Compute the expected value of <em>X</em> as follows:
Thus, the mean or expected value of <em>X </em>is 2.2.
(b)
Compute the value of E (X²) as follows:
Compute the standard deviation of <em>X</em> as follows:
Thus, the standard deviation of <em>X</em> is 1.3.
Because the two angles on the right add to 180 degrees, we can create this system:
We can also prove that
, which, when solved, shows that 
.
When plugged in to the original equation, we find that y = 105 degrees.
We can also prove that
When plugged in to the original equation, we find that y = 105 degrees.