Answer:
As confidence level decreases, the interval width decreases too.
Step-by-step explanation:
The confidence interval is an interval in which is probable that the true value of an unknown variable is contained. The confidence level is the probability that this true value is within the limits of the interval.
The degree of confidence or confidence level is defined and affects the width of the confidence interval.
If the true value of the mean foot length is within 21.71 and 25.09 with a 95% confidence level, if we decrease the confidence level to 90%, we expect to have an interval with smaller width.
When we increase the confidence level, we expect to be more sure about the true value being contained in the interval. As we do not count with new information, the only way to be more sure is to have a wider interval.
If the confidence level decreases, we can have a narrower confidence interval as we are not so severe with the probability of containing the true level.
As given in the picture, the formula for a cube's surface area is
, which s is the length of one side of the cube. So let's solve:
Answer:
<em>5.33 secs</em>
Step-by-step explanation:
Given the equation of the height modeled by the equation/
h(t) = -3.2 + 12.5t + 24.8
The object strikes the ground when the height h(t) is zero
Substituting h(t) = 0 into the expression
h(t) = -3.2t² + 12.5t + 24.8
0 = -3.2t² + 12.5t + 24.8
-3.2t² + 12.5t + 24.8 = 0
Multiply through by minus sign
3.2t² - 12.5t - 24.8 = 0
From the expression a = 3.2, b = -12.5 and c = -24.8
t = -(-12.5)±√(-12.5)²-4(3.2)(-24.8)/2(3.2)
t = 12.5±√156.25+317.44)/6.4
t = 12.5±√473.69/6.42
t = 12.5±21.76/6.42
t = 12.5+21.76/6.42
t = 34.26/6.42
t = 5.33secs
<em>Hence the object strike the ground after 5.33 secs</em>
Sample size= n= 84
sample mean= x = 107 s
population standard deviation =σ= 11.7
As, population standard deviation is given so we use the estimate:
x(+/-) z(α/2)(σ/√n)
At 99% Confidence interval means significance level is α=1-0.99= 0.01
So,
α/2=0.005
Now, z at α/2=0.005
z= 2.576
Now, by putting values
107(+/-)((2.576)(11.7/√84))
( 107-((2.576)(11.7/√84)), 107+((2.576)(11.7/√84)) )
(103.7, 110.288)
The answer would be Always
Hope this helped! :D
