A stadium asked for $760,000 for naming rights. During a bidding war for the stadium naming rights, one company bid 7% more than
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Answer:
One can be 99% confident the true mean shell length lies within the above interval.
The population has a relative frequency distribution that is approximately normal.
Step-by-step explanation:
We are given that Time-depth recorders were deployed on 6 of the 76 captured turtles. These 6 turtles had a mean shell length of 51.3 cm and a standard deviation of 6.6 cm.
The pivotal quantity for a 99% confidence interval for the true mean shell length is given by;
P.Q. = ~
where, = sample mean shell length = 51.3 cm
s = sample standard deviation = 6.6 cm
n = sample of turtles = 6
= true mean shell length
Now, the 99% confidence interval for =
Here, = 1% so
= 0.5%. So, the critical value of t at 0.5% significance level and 5 (6-1) degree of freedom is 4.032.
<u>So, 99% confidence interval for</u> =
= [51.3 - 10.864 , 51.3 + 10.864]
= [40.44 cm, 62.16 cm]
The interpretation of the above result is that we are 99% confident that the true mean shell length lie within the above interval of [40.44 cm, 62.16 cm].
The assumption about the distribution of shell lengths must be true in order for the confidence interval, part a, to be valid is that;
C. The population has a relative frequency distribution that is approximately normal.
This assumption is reasonably satisfied as the data comes from the whole 76 turtles and also we don't know about population standard deviation.
Answer:
<h3>AC=96 units.</h3>Step-by-step explanation:
We are given a parallelogram ABCD with diagonals AC and BD intersect at point E.
, and CE=6x .
<em>Note: The diagonals of a parallelogram intersects at mid-point.</em>
Therefore, AE = EC.
Plugging expressions for AE and EC, we get
Subtracting 6x from both sides, we get
Factoriong quadratic by product sum rule.
We need to find the factors of -16 that add upto -6.
-16 has factors -8 and +2 that add upto -6.
Therefore, factor of quadratic is (x-8)(x+2)=0
Setting each factor equal to 0 and solve for x.
x-8=0 => x=8
x+2=0 => x=-2.
We can't take x=-2 as it's a negative number.
Therefore, plugging x=8 in EC =6x, we get
EC = 6(8) = 48.
<h3>AC = AE + EC = 48+48 =96 units.</h3>