Let x be a continuous random variable that follows a distribution skewed to the left with...

Let x be a continuous random variable that follows a distribution skewed to the left with ?= 92 and ?=15. Assuming n/N <= .05, find the probability that the sample mean, x bar, for a random sample of 62 taken from this population will be (ROUND ANSWERS TO FOUR DECIMAL PLACES):

a) less than 81.5

P(less that 81.5)=

b) greater than 89.7

P(greater than 89.7)=

Please show your work.

Solutions

Expert Solution

Solution :

Given that ,

mean = = 92

standard deviation = = 15

n = 62

= = 92

= / n = 15 / 62 = 1.9050

a ) P( < 81.5) = P(( - ) / < (81.5-92) /1.9050 )

= P(z < -5.51) =0

probability = 0.0000

b ) P( > 89.7 ) = 1 - P( < 89.7 )

= 1 - P[( - ) / < (89.7-92) /1.9050 ]

= 1 - P(z <-1.21 )

= 1- 0.1131 = 0.8869

probability = 0.8869

orchestra answered 1 year ago

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