Question

Assume that the distribution of starting salaries for newly qualified CA’s is approximately Normal and has a std deviation of $2,500. We have a random sample of 16 CA’s.

a) Find the probability that the std error (sample std deviation) > $3000.

b) Find the probability that the std error (sample std deviation) < $1500.

Answer 1

a)

Sample Size,   n=   16          
Standard Deviation,   σ= 2500
                  
P ( s > 3000    ) = 1 - P( s ≤ 3000)=1 - P(X²≤(n-1)s²/σ²) = 1 - P(X² ≤ 15*3000²/2500² )
                  
   =1 - P(X² ≤   21.6   )      
   =1 -    0.88127 =   0.1187

[excel function: "=1 - CHISQ.DIST(21.6,15,TRUE)

b)

Sample Size,   n=   16      
population Standard Deviation,   σ= 2500   
              
P ( s< 1500 )= P(X²≤(n-1)s²/σ²) =       
              
   =P(X² < 5.4   ) =   0.0118

[excel function: "=CHISQ.DIST(5.4,15,TRUE) ]