PLEASE KINDLY DO BOTH QUESTIONS. THANK YOU IN ADVANCE. 1) The time that a randomly selected individual waits for an elev

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PLEASE KINDLY DO BOTH QUESTIONS. THANK YOU IN ADVANCE.
1) The time that a randomly selected individual waits for
an elevator in an office building has a uniform distribution over
the interval from 0 to 1 minute. For this
distribution 𝜇 = 0.5 and 𝜎 = 0.289.
(a) Let x be the sample mean waiting time for
a random sample of 15 individuals. What are the mean and
standard deviation of the sampling distribution of x?
(Round your answers to three decimal places.)
(b) Answer Part (a) for a random sample
of 55 individuals. (Round your answers to three decimal
places.)
2)
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 = 8850 and estimated
standard deviation 𝜎 = 3000. 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) Suppose a doctor uses the average x for two
tests taken about a week apart. What can we say about the
probability distribution of x?
The probability distribution of x is
approximately normal with 𝜇x = 8850
and 𝜎x = 3000.The probability
distribution of x is approximately normal
with 𝜇x = 8850
and 𝜎x =
1500.00. The probability distribution
of x is approximately normal
with 𝜇x = 8850
and 𝜎x = 2121.32.The probability
distribution of x is not normal.
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.)


(d) Compare your answers to parts (a), (b), and (c). How did the
probabilities change as n increased?
The probabilities stayed the same
as n increased.The probabilities increased
as n increased. The
probabilities decreased as n increased.