9. Assume random variable x follows a probability distribution shown in the tabl
ID: 3130798 • Letter: 9
Question
9. Assume random variable x follows a probability distribution shown in the table below. Determine the mean and standard deviation of x. Show all work. Just the answer, without supporting work, will receive no credit.
x
-2
0
1
3
5
P (x)
0.1
0.2
0.3
0.1
0.3
11. Assume the weights of men are normally distributed with a mean of 172 lb and a standard deviation of 30 lb. Show all work. Just the answer, without supporting work, will receive no credit.
(a) Find the 80th percentile for the distribution of men’s weights.
(b) What is the probability that a randomly selected man is greater than 185 lb?
12. Assume the IQ scores of adults are normally distributed with a mean of 100 and a standard deviation of 15. Show all work. Just the answer, without supporting work, will receive no credit.
(a) If a random sample of 25 adults is selected, what is the standard deviation of the sample mean?
(b) What is the probability that 25 randomly selected adults will have a mean IQ score that is between 95 and 105?
13. A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a 95% confidence interval estimate of the proportion of adults believing in global warming. Show all work. Just the answer, without supporting work, will receive no credit.
x
-2
0
1
3
5
P (x)
0.1
0.2
0.3
0.1
0.3
Explanation / Answer
9.
Consider:
Thus,
E(x) = Expected value = mean = Sum(xP(x)) = 1.9 [ANSWER]
Also,
Var(x) = E(x^2) - E(x)^2 = 5.49
Hence,
s(x) = sqrt [Var(x)] = 2.343074903 [ANSWER, STANDARD DEVIATION]
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x P(x) x P(x) x^2 P(x) -2 0.1 -0.2 0.4 0 0.2 0 0 1 0.3 0.3 0.3 3 0.1 0.3 0.9 5 0.3 1.5 7.5Related Questions
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