statistics

Question

Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood in a healthy adult. Then mu=7500 and o = 1750. A random sample of n=50 workers from the toxic cleanup site were given a blood test that showed x bar=6820.

 

compute P(x bar< 6820)

 

I know I have to get a new standard deviation

           make a graph

           need a new z score

 

on my graph I got                 -3         -2       -1         0        1           2             3

                                         2250     4000   5750    7500    9250    11,000     12,750

 

then I did 6820-7500/1750 and I got 680/1750 or 0.338, where did I miss a step?

Answer 1

they tell you x bar = sample mean = 6820

7500 = the population mean

1750 = population standard deviation

sample size = 50= N

convert 1750 to the sample standard deviation, s, by dividing by square root of N= sqr50

s = 1750/sqr50 = 1750/5sqr2 = 350/sqr2

z = (6820-7500)/350/sqr2 = -680/350/sqr2= -68sqr2/35 =-2.7476

z= about -2.75

convert to area under the curve would be the next step in calculating a probability. do that with a z table or z calculator

P(x bar < mu)= area below the normal curve in the tail below x bar = nearly zero = very small percentage

= about .0030 = 0.3 %