PLEASE ANSWER ASAP!!!The grid you see below is in the shape of a rectangle. What is the area, in square units, of the shaded par
t?
1 answer:
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Answer:
(a) A 95% confidence interval for the population mean is [433.36 , 448.64].
(b) A 95% upper confidence bound for the population mean is 448.64.
Step-by-step explanation:
We are given that article contained the following observations on degrees of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:
420, 425, 427, 427, 432, 433, 434, 437, 439, 446, 447, 448, 453, 454, 465, 469.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~
where, = sample mean =
= 441
s = sample standard deviation = = 14.34
n = sample size = 16
= population mean
<em>Here for constructing a 95% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.</em>
<em />
<u>So, 95% confidence interval for the population mean, </u><u> is ;</u>
P(-2.131 < < 2.131) = 0.95 {As the critical value of t at 15 degrees of
freedom are -2.131 & 2.131 with P = 2.5%}
P(-2.131 < < 2.131) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u>95% confidence interval for</u> = [
,
]
= [ ,
]
= [433.36 , 448.64]
(a) Therefore, a 95% confidence interval for the population mean is [433.36 , 448.64].
The interpretation of the above interval is that we are 95% confident that the population mean will lie between 433.36 and 448.64.
(b) A 95% upper confidence bound for the population mean is 448.64 which means that we are 95% confident that the population mean will not be more than 448.64.
Answer: On the 29th day
Step-by-step explanation:
According to this problem, no lilypad dies and the lilypads always reproduce, so we can apply the following reasoning.
On the first day there is only 1 lilypad in the pond. On the second day, the lilypad from the first reproduces, so there are 2 lilypads. On day 3, the 2 lilypads from the second day reproduce, so there are 2×2=4 lilypads. Similarly, on day 4 there are 8 lilypads. Following this pattern, on day 30 there are 2×N lilypads, where N is the number of lilypads on day 29.
The pond is full on the 30th day, when there are 2×N lilypads, so it is half-full when it has N lilypads, that is, on the 29th day. Actually, there are lilypads on the 30th, and
lilypads on the 29th. This can be deduced multiplying succesively by 2.