For large sample confidence intervals about the mean you have:
xBar ± z * sx / sqrt(n)
where xBar is the sample mean z is the zscore for having α% of the data in the tails, i.e., P( |Z| > z) = α sx is the sample standard deviation n is the sample size
We need only to concern ourselves with the error term of the CI, In order to find the sample size needed for a confidence interval of a given size.
z * sx / sqrt(n) = width.
so the z-score for the confidence interval of .98 is the value of z such that 0.01 is in each tail of the distribution. z = 2.326348
The equation we need to solve is:
z * sx / sqrt(n) = width
n = (z * sx / width) ^ 2.
n = ( 2.326348 * 6 / 3 ) ^ 2
n = 21.64758
Since n must be integer valued we need to take the ceiling of this solution.
n = 22
Answer:
a) 
b) 
c) 
d) E(3X + 2) = 21.35
e) 
f) V(3X+2) = 140.832
g) E(X+1) = 7.45
h) V(X+1) = 15.648
Step-by-step explanation:
a) 

b)

c)

d)

e)

f)

g)

h)

Answer:
x>4
Step-by-step explanation:
x+3>19-3x
x+3x>19-3
4x>16
x>4
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Answer:
y^6
Step-by-step explanation:
When multiplying terms with exponents that have the same base, the rule is to add the exponents. y * y^3 * y^2 = y^(1 + 3 + 2). (remember that y has a hidden exponent of 1, we just don't write that because it is redundant and unnecessary). y^(1 + 3 + 2) = y^6
hope this helps! <3