Question

Workers at a large toxic cleanup project are concerned that their white blood cell counts may have been reduced. Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood in a healthy adult. Then μ = 7500 and σ ≈ 1750.† A random sample of n = 50 workers from the toxic cleanup site were given a blood test that showed x = 6820. What is the probability that, for healthy adults, x will be this low or lower? (a) How does the central limit theorem apply? Explain. The central limit theorem describes the distribution of x as normal with mean μ x = 7500 and σ x ≈ 35.0. The central limit theorem describes the distribution of x as normal with mean μ x = 7500 and σ x ≈ 247.5. The central limit theorem does not apply because the sample size is too small. The central limit theorem describes the distribution of x as normal with mean μ x = 7500 and σ x ≈ 1750.0. Correct: Your answer is correct. (b) Compute P(x ≤ 6820). (Round your answer to four decimal places.) P(x ≤ 6820) = (c) Based on your answer to part (b), would you recommend that additional facts be obtained, or would you recommend that the workers' concerns be dismissed? Explain. Yes, it would be reasonable to gather additional facts. The probability that the 50 workers' average white blood cell count is 6820 or lower, if they were healthy adults, is extremely low. Yes, it would be reasonable to gather additional facts. The probability that the 50 workers' average white blood cell count is 6820 or lower, if they were healthy adults, is extremely large. No, it would not be necessary to gather additional facts. The probability that the 50 workers' average white blood cell count is 6820 or lower, if they were healthy adults, is extremely low. No, it would not be necessary to gather additiona

Answer 1

sample size       =n=	50
std error=σx̅=σ/√n=	247.4874

a)

The central limit theorem describes the distribution of x as normal with mean μ x = 7500 and σ x ≈ 247.5.

b)

for normal distribution z score =(X-μ)/σ

probability =

P(X<6820)

=

P(Z<-2.75)=

0.0030

c)

  Yes, it would be reasonable to gather additional facts. The probability that the 50 workers' average white blood cell count is 6820 or lower, if they were healthy adults, is extremely low.