Question

For a woman in Lafayette, the mean salary with an Associate of Applied Science (AAS) is $53,403 with standard deviation $4,518 . Assuming a normal distribution, answer the following. Recall that a probability with more than three zeros will round to two places past the requisite zeros.

Step 1 of 4: What salary would put a woman in the 67th percentile of Associate of Applied Science (AAS) holders in Lafayette? Answer(How to Enter)2 Points

Step 2 of 4:

What salary would put a woman in the top 8% of Associate of Applied Science (AAS) holders in Lafayette?

Step 3 of 4:

What is the probability that a woman with an Associate of Applied Science (AAS) will make a salary that is between minimum wage and twice minimum wage? [The state minimum wage is $7.25/hour. Assume 40 hours/week with no leave.]

Step 4 of 4:

Think about your answer for the last step. Was the event unusual? What does that imply for this demographic?
For bonus points, consider that the poverty line for a family of 4 is $25,750 and discuss whether a single earner with this degree can support a family of 4; use the distribution to justify your answer.

Answer 1

Step 1 of 4:

z = 0.44

0.44 = (x - 53403)/4518

x = 0.44*4518 + 53403 = 55390.53

Step 2 of 4:

z = 1.41

1.41 = (x - 53403)/4518

x = 1.41*4518 + 53403 = 59751.11

Step 3 of 4:

x = 7.25*40*52 = 15080

2x = 15080*2 = 30160

z = (15080 - 53403)/4518 = -8

P (z = -8) = 0.0000

z = (30160 - 53403)/4518 = -5

P (z = -5) = 0.0000

Required probability = 0.0000

Step 4 of 4:

Yes, the event is unusual because no one is makinga salary that is between minimum wage and twice minimum wage.

Bonus =

z = (25750 - 53403)/4518 = -6

P (z = -6) = 0.0000

Thus, this single earner with this degree cannot support a family of 4.