Test 02 Normal Curves Chapter 7.3 • Name:

1. For the following curves A, B, and C determine the mean and the standard deviation σ:
t2 (14K)

CurveMean standard deviation σ
A  
B  
C  

2. Twelve fruit bats from the lagoon islands of Chuuk state were measured and found to have a mean skull length of 44.708 mm with a standard deviation σ of 0.593 mm. Presume that the distribution of skull lengths is normally distributed about the mean.

  1. __________ What is the probability a lagoon fruit bat will have a skull length shorter than 44.115 mm?
  2. __________ What is the probability a lagoon fruit bat will have a skull length longer than 45.880 mm?
  3. __________ What will be the length x shorter than which the shortest 2.28% (0.0228) of the lagoon bat skulls will be found?
  4. __________ What will be the length x beyond which the longest 5% of the lagoon bat skulls will be found?
Statistic or ParameterSymbolEquationsExcel
Calculate a z value from an xz = Calculate z from x =STANDARDIZE(x, , σ)
Calculate an x value from a z x= z * σ + = z*σ+
Find a probability p from a z value (the area to the left of z) =NORMSDIST(z)
Find a z value from a probability p (from the area p to the left of z) =NORMSINV(p)

Standard normal distribution Excel: Left to z