Question

Please help, I do not understand how to do this:
Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 7400 and estimated standard deviation σ = 2900. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)

(b)What is the probability of x < 3500? (Round your answer to four decimal places.)

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

Answer 1

(A) From the problem statement, N(7400, 2900).

P(X < 3500) = .0893

(B) ... .0893?

(C)
This is a test of means. For this we make a new distribution, N(xbar, s), where xbar = mu, s = sigma / sqrt(n).

N(7400, 1674.32)
P(X < 3500) = .0099

Answer 2

Note: For part c, the probability statement should read P(xbar < 3500). The bar denotes sampling means.

Answer 3

Thank you so much, I appreciate it!