### Quiz 07 Normal Curves 7.3 • Name:

1. For the following curves A, B, and C determine the mean µ and the standard deviation σ:

CurveMean µstandard deviation σ
A
B
C

2. According to a presentation on the Asian Development Bank Economic Report on the FSM done in 2005, investment in the fishing industry, primarily tuna fishing, by the FSM resulted in a mean loss µ of 3.874 million dollars per year with a standard deviation σ of 2.938 million dollars per year. Presume that the data is normally distributed.

1. p(x>3.874)=__________ What is the probability the loss was greater than 3.874 million dollars in any given year?
2. p(x<0.936)=__________ What is the probability that the loss was less than 0.936 million dollars in any given year?
3. p(x<0.000)=__________ What is the probability that the loss was less than 0.000 million dollars in any given year? This probability estimates the probability that the FSM could make money by investing in the tuna industry. Use Excel to answer this!
4. x = __________ What will be the minimum value for the top 20% of the losses the FSM could sustain by investing in tuna? Nota bene (hint): This is a backwards problem: set the highest 20% as the area and work backwards to find the x value!

Normal Statistics
Calculate a z value from an x z = =STANDARDIZE(x, µ, σ)
Calculate an x value from a z x = z σ + µ =z*σ+µ
Find a probability p(x) from a z value where the probability p is the area to the left of z.     =NORMSDIST(z)
Find a z value from a probability p, where p is the area to the left of z     =NORMSINV(p)