workers at a large toxic cleanup project are concerned that their white blood cell counts may have been reduced. The white blood cell count in the general population is known to have a mean of 7500 cells/mL with a standard deviation of 1750cells/mL

Question

a)what is the probability of a random person in the general population having a white cell count as low or lower than 6820cells/mL?
i got 0.3485. Is this correct?

A random sample of 50 workers was taken.
b)If the general population value holds for the workers state the mean and standard deviation of this sampling distribution. Sketch the sampling distribution of the mean.

Are these values the same as in main intro of questions? Also what should i include in the sketch?

c)What is the probability that the sample of the workers at the cleanup site would have a mean white cell count of 6280cells/mL?

i got 0.0030 but not sure what to do cause the question DOES NOT say above or below but would have a mean of 6280cell/ml.

d)would these calculations be valid if
the pop. dist. was skewed?

Thanks

Answer 1

a. Z = (score-mean)/SD = (6820-7500)/1750 = -.39

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability of the Z score = .3483.

b. Mean the same, but SEm = SD√n. Standard Error of mean = your SD

c. DK

d. Z scores only apply to norm distributions.