A random variable X follows the uniform distribution with a lower limit of 750 a
ID: 3254664 • Letter: A
Question
A random variable X follows the uniform distribution with a lower limit of 750 and an upper limit of 850.
Calculate the mean and the standard deviation for the distribution. (Round intermediate calculation for Standard deviation to 4 decimal places and final answer to 2 decimal places.)
What is the probability that X is less than 840? (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
Approximately 76% of baby boomers aged 43 to 61 are still in the workforce (The Boston Globe, July 10, 2008). Six baby boomers are selected at random.
What is the probability that exactly one of the baby boomers is still in the workforce? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)
What is the probability that at least five of the baby boomers are still in the workforce? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)
What is the probability that less than two of the baby boomers are still in the workforce? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)
What is the probability that more than the expected number of the baby boomers are still in the workforce? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)
A random variable X follows the uniform distribution with a lower limit of 750 and an upper limit of 850.
Explanation / Answer
Solution2:
binomial distr
n=6
p=probability oif success=0.76
q=1-p=probability of failure=1-0.76=0.24
P(X=1)
=6C1(0.76)1 (1-0.76)6-1
=6*0.76*0.24^5
=0.0036
PROBABILITY=0.0036
Solution2b:
P(X>=5)
P(X=5)+P(X=6)
=6C5(0.76)5 (1-0.76)6-5 +6C6(0.76)6 (1-0.76)6-6
=0.5578
PROBABILITY=0.5578
SOLUTION2C:
P(X<2)
=P(X=0)+P(X=1)
=6C0(0.76)0 (0.24)^6-0 +6C1(0.76)^1(0.24)^6-1
=0.0038
PROBABILITY=0.0038
SOLUTION2D:
MEAN=np=6*0.76=4.56=5
that is
P(X=5)+P(X=6)
=0.5578
PROBABILITY=0.5578
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