The values of serum sodium in healthy adults approximately f

The values of serum sodium in healthy adults approximately follow a normal distribution with a mean of 141 mEq/L and a standard deviation of 3mEq/L. What is probability that a normal healthy adult will have a serum sodium value above 147 mEq/L? What is the probability that a normal healthy adult will have a serum sodium value below 130 mEq/L? What is the probability that a normal healthy adult will have a serum sodium value between 132 and 150m/EqL? What serum sodium level is necessary to put someone in the top 1 % of the distribution? What serum sodium level is necessary to put someone in the bottom 10% of the distribution?

Solution

a) using NORMDIST function in excel, we get 0.97725. Then subtract this with 1

P(x>147)=0.02275

b) Using NORMDIST function in excel, we get 0.00012.

c) Using NORMDIST function for both the values and subtract them

P(132<x<150)=0.99865-0.00135=0.9973.

d) Using NORMSINV(1-0.01)=2.3263

2.3263=x-141/3

2.3263*3=x-141

x=147.9 so approximately 150.

e) Using NORMSINV(0.1)=-1.2815

-1.2815=x-141/3

solving for x we get

x=137.1 so approximately 137.