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Answer:
99% confidence interval for the population proportion of employed individuals is [0.104 , 0.224].
Step-by-step explanation:
We are given that a simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week.
Of the 250 employed individuals surveyed, 41 responded that they did work at home at least once per week.
Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;
P.Q. = ~ N(0,1)
where, = sample proportion of individuals who work at home at least once per week =
= 0.164
n = sample of individuals surveyed = 250
<em>Here for constructing 99% confidence interval we have used One-sample z proportion statistics.</em>
So, 99% confidence interval for the population proportion, p is ;
P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5%
level of significance are -2.5758 & 2.5758}
P(-2.5758 < < 2.5758) = 0.99
P( <
<
) = 0.99
P( < p <
) = 0.99
<em>99% confidence interval for p</em> = [ ,
]
= [ ,
]
= [0.104 , 0.224]
Therefore, 99% confidence interval for the population proportion of employed individuals who work at home at least once per week is [0.104 , 0.224].
It the wiper blade (and arm) made a full rotation, 2 circles would be formed.
One small circle with radius b, and a larger circle with radius a+b.
The areas of these 2 circles are respectively:
and
120° is 1/3 of a complete angle 360° which form a circle, so the areas formed by the arm of length b, and the arm + the wiper blade (a+b) are:
and 
in squared respectively.
the actual wiped area is
(in squared)
Area of the window is 54*24= 1296 (in squared)
thus, the ratio of the wiped area to the whole area of the window is 351.7/1296=0.271
Converted to percentages, this is 27.1%
Answer: 27.1%
One small circle with radius b, and a larger circle with radius a+b.
The areas of these 2 circles are respectively:
120° is 1/3 of a complete angle 360° which form a circle, so the areas formed by the arm of length b, and the arm + the wiper blade (a+b) are:
the actual wiped area is
Area of the window is 54*24= 1296 (in squared)
thus, the ratio of the wiped area to the whole area of the window is 351.7/1296=0.271
Converted to percentages, this is 27.1%
Answer: 27.1%