6.21. Help on statistical normal probability distribution problem?

Cerebral Blood Flow (CBF) in brains of healthy people is normally distributed with a mean of 74 an a stand dev of 16.


a. What proportion of healthy people will have CBF readings between 60 and 80?


b. What proportions of healthy people will have CBF reading above 100?


c. If a person has a CF reading below 40, he is classified as at risk for a stroke. What proportion of healthy people will mistakenly be diasgnosed as "at risk"?





Answers at back of book:


a. .4586 b. .0526 c. .0170





I have a solutions manual but it doesn't include this question. Please give a step by step instruction how to get to the answer and I'll give you 10 pts. Thanks.

6.21. Help on statistical normal probability distribution problem?
Let X be the CBF, X ~ Normal(μ =74, σ = 16)


Let Z be the standard normal, Z ~ N(0 , 1)





To solve these questions you have to translate the values to standard units. My numbers are a little different because I did not round up or down any the z-scores and used software, MINITAB, to get the values for the probabilities.





a) find P[60 %26lt; X %26lt; 80]


= P[ (60 - 74)/16 %26lt; Z %26lt; (80 - 74)/16]


= P[-0.875 %26lt; Z %26lt; 0.375]


= P[Z %26lt; 0.375] - P[Z %26lt; -0.875]


= 0.646170 - 0.190787


= 0.455383





b) find P[ X %26gt; 100]


= P[ Z %26gt; (100 - 74)/16 = 1.625] = 0.052081





c) P[X %26lt; 40] = P[Z %26lt; -2.125] = 0.0167933