An Egyptian pyramid has a square base that measures 80 meters on each side. If the height of the pyramid is 30 meters, what is t
1 answer:
You might be interested in
Answer:
The value is
Step-by-step explanation:
From the question we are told that
The amount charge per year is
The number of members it will have at this amount is
The amount amount increase that will lead to the loss of a single member is
Generally the total amount the club would obtain from its members is mathematically represented as
Now let x denote the number of member lost
Hence
=>
=>
Thus the number of members that be removed to give the maximum income from dues is obtained by differentiating the above equation and equating it to zero
=>
So from we have
So the amount the club should charge is
Answer:
(a) 80% confidence interval for the population mean is [109.24 , 116.76].
(b) 80% confidence interval for the population mean is [109.86 , 116.14].
(c) 98% confidence interval for the population mean is [105.56 , 120.44].
(d) No, we could not have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed.
Step-by-step explanation:
We are given that a simple random sample of size n is drawn from a population that is normally distributed.
The sample mean is found to be 113 and the sample standard deviation is found to be 10.
(a) The sample size given is n = 13.
Firstly, the pivotal quantity for 80% confidence interval for the population mean is given by;
P.Q. = ~
where, = sample mean = 113
s = sample standard deviation = 10
n = sample size = 13
= population mean
<em>Here for constructing 80% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>
<u>So, 80% confidence interval for the population mean, </u><u> is ;</u>
P(-1.356 < < 1.356) = 0.80 {As the critical value of t at 12 degree
of freedom are -1.356 & 1.356 with P = 10%}
P(-1.356 < < 1.356) = 0.80
P( <
<
) = 0.80
P( <
<
) = 0.80
<u>80% confidence interval for </u> = [
,
]
= [ ,
]
= [109.24 , 116.76]
Therefore, 80% confidence interval for the population mean is [109.24 , 116.76].
(b) Now, the sample size has been changed to 18, i.e; n = 18.
So, the critical values of t at 17 degree of freedom would now be -1.333 & 1.333 with P = 10%.
<u>80% confidence interval for </u> = [
,
]
= [ ,
]
= [109.86 , 116.14]
Therefore, 80% confidence interval for the population mean is [109.86 , 116.14].
(c) Now, we have to construct 98% confidence interval with sample size, n = 13.
So, the critical values of t at 12 degree of freedom would now be -2.681 & 2.681 with P = 1%.
<u>98% confidence interval for </u> = [
,
]
= [ ,
]
= [105.56 , 120.44]
Therefore, 98% confidence interval for the population mean is [105.56 , 120.44].
(d) No, we could not have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed because t test statistics is used only when the data follows normal distribution.