Answer: The 95% confidence interval for the mean of x is (94.08, 101.92) .
Step-by-step explanation:
We are given that ,
A random variable x has a Normal distribution with an unknown mean and a standard deviation of 12.
i.e.
Also, it is given that , Sample mean having sample size : n= 36
For 95% confidence ,
Significance level :
By using the z-value table , the two-tailed critical value for 95% Confidence interval :
We know that the confidence interval for unknown population mean is given by :-
, where = Sample mean
= Population standard deviation
= Critical z-value.
Substitute all the given values, then the required confidence interval will be :
Therefore, the 95% confidence interval for the mean of x is (94.08, 101.92) .
The percent error is 53.3 %
<em><u>Solution:</u></em>
<em><u>The formula for percent error is given as:</u></em>
From given,
A political analyst predicts Mr. Smith will only get 122 votes for mayor
Mr. Smith only gets 57 votes
Therefore,
Theoretical = 122
Experimental = 57
Thus we get,
Thus percent error is 53.3 %
Answer: D) 52%
Step-by-step explanation:
G = gymnastics
B = baseball
S = soccer
G = 28%
BA = 29%
S = 19%
G and BA = 14%
BA and S = 12%
G and S = 10%
GBS = 8%
So, as we can see at the Venn diagram attached (consider every number in %)
GBS = 8
A = G and S - GBS = 10 - 8 = 2
B = G and BA - GBS = 14 - 8 = 6
C = BA and S - GBS = 12 - 8 = 4
Only G = G - A - B - GBS = 28 - 2 - 6 - 8 = 12
Only BA = BA - B - C - GBS = 29 - 6 - 4 - 8 = 11
Only S = S - A - C - GBS = 19 - 2 - 4 - 8 = 5
So, 2+6+4+12+11+5+8 = 48
100 - 48 = 52%
So you have to find the volume of the tank, and the volume of the pyramid. Then subtract the volume of the pyramid from that out of the tank. The formula for pyramid is v = lwh/3. For the tank (which is a cube in this case) It's any given side cubed.
40*30*30 = 3600/3=1200cm cubed
40^3 = 6400cm cubed
6400-1200=5200cm^3 of water
(If you don't get this answer then I may have made a calculation error as I did this quickly in my head, just check my answer and yours to see)