Urgent homework question?

For the sample mean, you use

sample mean standard deviation = population standard deviation/ sqrt(N)

where N is the number of samples

sample mean standard deviation = 3.6/sqrt(35) = 0.608511063

so for the sample

P( 34<x<37.5) = P(x< 37.5) - P(x< 34)

P(x< 37.5) =

z = (x – μ) / σ_sample_mean_

z= (37.5-36) / 0.608511063 = 2.465033243

P(x< 37.5) = P(z< 2.465)

P(z< 2.46) = 0.99286

P(z< 2.47) = 0.99305

so 2.4650 is in the exact middle difference = 0.99305-0.99286 = 0.00019

Divided by 2 = 0.000095 but rounding to five digits gives 0.00010

so at 0.00010 to 0.99286 = 0.99296

P(z<2.465) = approx. 0.99296

P(x< 37) = approx. 0.99296

P(x< 34 ) =

z = (34-36) / 0.608511063 = -3.286710991

from a z-table

P(z< -3.29) = 0.00050

P(z< -3.28) = 0.00052

so this is close enough to z= -3.29

P( z< -3.2867) = approx. 0.00052

P(x< 34) = approx. 0.00052

P( 34<x<37.5) = P(x< 37.5) - P(x< 34) = 0.99296 - 0.00052 = 0.99244

so the answer is 0.99244

if you class expect you to use a z-table but not interpolate

just use the closes values which would be 0.99305 - 0.00052 = 0.99253

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