Answer:
Yes, both np and n(1-p) are ≥ 10
Mean = 0.12 ; Standard deviation = 0.02004
Yes. There is a less than 5% chance of this happening by random variation. 0.034839
Step-by-step explanation:
Given that :
p = 12% = 0.12 ;
Sample size, n = 263
np = 263 * 0.12 = 31.56
n(1 - p) = 263(1 - 0.12) = 263 * 0.88 = 231.44
According to the central limit theorem, distribution of sample proportion approximately follow normal distribution with mean of p = 0.12 and standard deviation sqrt(p*(1 - p)/n) = sqrt (0.12 *0.88)/n = sqrt(0.0004015) = 0.02004
Z = (x - mean) / standard deviation
x = 22 / 263 = 0.08365
Z = (0.08365 - 0.12) / 0.02004
Z = −1.813872
Z = - 1.814
P(Z < −1.814) = 0.034839 (Z probability calculator)
Yes, it is unusual
0.034 < 0.05 (Hence, There is a less than 5% chance of this happening by random variation.
Answer:
Step-by-step explanation:
Since 
have the same denominators, we add them first. We then add 
to the result.
Answer:
The scale factor is 4.5
Step-by-step explanation:
Scale factor from ∆RST to ∆XYZ = side length of ∆XYZ / corresponding side length of ∆RST
Thus:
XY corresponds to RS
XY = 45
RS = 10
Therefore:
Scale factor = 45/10 = 4.5
Scale factor from ∆RST to ∆XYZ = 4.5
<span>z=5-2i
</span><span>|z| = [ (5^2 + (-2)^2) ] ^ 0.5
= ( 25+4) ^ 0.5
= 29^0.5 </span>
