1)
µ = 21.1
σ = 5.3
we need to calculate probability for ,
P ( 19 < X <
24 )
=P( (19-21.1)/5.3 < (X-µ)/σ < (24-21.1)/5.3 )
P ( -0.396 < Z <
0.547 )
= P ( Z < 0.547 ) - P ( Z
< -0.396 ) =
0.7079 - 0.3460 =
0.3619 (answer)
2)
µ= 1674
σ = 212.5
proportion= 0.2500
Z value at 0.25 =
-0.674 (excel formula =NORMSINV(
0.25 ) )
z=(x-µ)/σ
so, X=zσ+µ= -0.674 *
212.5 + 1674
X = 1530.6709
(answer)
3)
Z = (X - µ )/(σ/√n) = (
50000 - 50830.00 ) /
( 8520.000 / √ 50 )
= -0.69
P(X ≤ 50000 ) = P(Z ≤
-0.689 ) = 0.2455
(answer)
4)
Number of Items of Interest, x =
375
Sample Size, n = 814
Sample Proportion , p̂ = x/n =
0.4607
q = 1 - p=1-0.4607 = 0.5393
Level of Significance, α = 0.05
z -value = Zα/2 = 1.960 [excel
formula =NORMSINV(α/2)]
Standard Error , SE = √[p̂(1-p̂)/n] =
0.0175
margin of error , E = Z*SE = 1.960
* 0.0175 = 0.0342
95% Confidence Interval is
Interval Lower Limit = p̂ - E = 0.461
- 0.0342 = 0.4264
Interval Upper Limit = p̂ + E = 0.461
+ 0.0342 = 0.4949
95% confidence interval is (
0.4264 < p < 0.4949
)
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