The heights of 1000 students are approximately normally distributed with a mean of 174.5 cm and a standard deviation of 6.9 cm. suppose 200 random samples of size 25 are drawn from this population. determine the number of sample means that are expected to fall between 172.5 and 175.8 cm inclusive.

Mean ( u ) =174.5
Standard Deviation ( sd )=6.9/ Sqrt ( 25 )=1.38
Number ( n ) = 25
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 172.5) = (172.5-174.5)/6.9/ Sqrt ( 25 )
= -2/1.38
= -1.4493
= P ( Z <-1.4493) From Standard Normal Table
= 0.07363
P(X < 175.8) = (175.8-174.5)/6.9/ Sqrt ( 25 )
= 1.3/1.38 = 0.942
= P ( Z <0.942) From Standard Normal Table
= 0.82691
P(172.5 < X < 175.8) = 0.82691-0.07363 = 0.7533 

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