Question

The average length of a maternity stay in a U.S. hospital is said to be 2.2 days with a standard deviation of 0.9 days. We randomly survey 80 women who recently bore children in a U.S. hospital.

B)Give the distribution of

X.

(Round your standard deviation to two decimal places.)

C)Give the distribution of ΣX. (Round your standard deviation to two decimal places.)

Answer 1

X ~ N ( , )

Where = 2.2 , = 0.9

Therefore ,

X ~ ( 2.2 , 0.9)

~ N ( , / sqrt(n) )

Where = 2.2 ,

/ sqrt(n) = 0.9 / sqrt ( 80 ) = 0.10

~ ( 2.2 , 0.10 )

X ~ ( n , sqrt [ n 2 ] )

Where

n = 80 * 2.2 = 176

sqrt [ n 2 ] = sqrt ( 80 * 0.92 ) = 8.05

X ~ N ( 176 , 8.05 )