SOLUTION: Assume that blood pressure readings are normally distributed with μ = 111 and σ = 7. (a) A researcher wishes to select people for a study but wants to exclude the top 10% and bo

Question 1159627: Assume that blood pressure readings are normally distributed with μ = 111 and σ = 7.
(a) A researcher wishes to select people for a study but wants to exclude the top 10% and bottom 10% of the blood pressure readings. Find the upper and lower readings to qualify people to participate in the study.
(b) Another researcher is interested in the mean value of blood pressures from a group of people. Suppose 10 people are selected at random (without any selection criteria), calculate the probability of having the mean value above the upper bound reading which is calculated in part (a).
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z(0.10)=-1.28
z(.90)=+1.28
z=(x-mean)/sd
x-mean=-8.96 for lower
x=111-8.96=102 mm Hg for lower
x=111+8.96=120 mm Hg for upper
the sd of the sampling distribution would be 7/sqrt(10)=2.21
probability of mean being above 120 mm would be a z=(120-111)/2.21=9/2.21=4.07
probability z>4.07 is about 2 x 10^-5 or 0.000023
I rounded the mm Hg to the nearest integer, because BP cannot be measured with a cuff to less than a mm accuracy, if that.
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