I need help for #1 (an explanation would be great too).

±6i√2

Step-by-step explanation:

Recall that the square root of a negative number is imaginary, which is shown by the use of "i."

Examples:  √4 = ±2; √4 = i√4 = ±i2

Then √72 = ±√36√2 = ±6√2, and

      √(-72) = ± i√36√2 = ±6i√2

Note that this is identical to the result shown in the problem:  √(36·2·(-1) )

0.1003

Step-by-step explanation:

Mean salary = u = $ 50,000

Standard Deviation = = $ 6,000

Top 10% of the new graduates make a salary of $57,680. We have to find the probability that the salary of new graduate is $57,680 or more. We can find this by converting this score to equivalent z score and using the z table to find the probability of z score being higher than this value, as shown below:

The formula for z score is:

Using the values, we get:

Thus,

P(Salary ≥ 57680) = P(z ≥ 1.28)

Now, using the z table, the probability of z score being higher than 1.28 comes out to be: 0.1003

So,

P( z ≥ 1.28 ) = P(Salary ≥ 57680) = 0.1003

Thus, the probability of earning a salary of atleast 57,680 is 0.1003