Assume that the distribution of starting salaries for newly qualified CA’s is approximately Normal and has...

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Assume that the distribution of starting salaries for newlyqualified 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 stddeviation) > $3000.
b) Find the probability that the std error (sample stddeviation) < $1500.

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4.2 Ratings (822 Votes)

Sample Size,   n=   16
Standard Deviation,   ?= 2500

P ( s > 3000    ) = 1 - P( s ? 3000)=1 - P(X²?(n-1)s²/?²) = 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)

Sample Size,   n=   16
population Standard Deviation,   ?= 2500

P ( s< 1500 )= P(X²?(n-1)s²/?²) =

   =P(X² < 5.4   ) =   0.0118

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

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