Answer:
a) the proportion of 95% confidence intervals that include the population proportion approaches 0.95
b) Sample proportion does not include the population proportion then the sample proportion is more than 1.96 standard error from the population proportion
Step-by-step explanation:
a)
Given the the data in the question, confidence level is 95%.
In this case as the number of samples increases, the proportion of 95% confidence intervals that include the population proportion approaches 0.95. hence the expected value of the proportion.
b)
Given the the data in the question, confidence level is 95% and sample proportion
we know that In normal distribution 68% confidence indicate one standard deviation, 95% confidence indicate 2 standard deviation while 99.97% confidence indicate 3 standard deviation.
The sample proportion does not include the population proportion, in 95% confidence from the standard normal table 0.95 value lies within the critical value of 1.96 approximately 2.
hence ( z =2 ) that satisfied the 1.96 standard error from the population proportion
hence, Sample proportion does not include the population proportion then the sample proportion is more than 1.96 standard error from the population proportion
<u>Given</u>:
Let the 3 consecutive even integers be x, x + 2 and x + 4.
Given that the sum of the squares of the first and the second integers is 2 more than the third integer.
We need to determine the 3 consecutive integers.
<u>Value of x:</u>
From the given, the expression can be written as,
Simplifying, we get;
Factoring the middle term, we get;
Since, the fraction is neither a even nor odd integer.
Thus, the value of x is -2.
<u>Consecutive integers:</u>
Substituting the value of x in the consecutive integers x, x + 2 and x + 4, we get;
Thus, the 3 consecutive integers are -2, 0 and 2.
If x = 16 and y = -16, then x+y = 16+(-16) = 0
Alternatively, if x = -16 and y = 16, then x+y = -16+16 = 0
So y = -x and x can be equal to either 16 or -16
Answer:
angle of refraction at first surface is 22.74°
Step-by-step explanation:
Given data
thickness = 1.50 cm
n = 1.52
angle = 36.0°
to find out
angle of refraction at first surface
solution
we will apply here Snells law that is
n1 sinθ1 = n2 sinθ2
θ2 = sin^-1 ( n1/n2) sin θ1
here n1 is 1 and n2 is 1.52 and θ1 = 36.0°
θ2 = sin^-1 ( n1/n2) sin θ1
θ2 = sin^-1 ( 1 / 1.52 ) sin36
θ2 = 22.74°
angle of refraction at first surface is 22.74°
V=hpir^2
r=10
v=6283
6283=hpi10^2
6283=100hpi
divide both sides by 100
62.83=hpi
aprox pi=3.141592
divide both sides by pi
19.9994143=h
so about 20 inches