In: Statistics and Probability
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.
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