Answer:
StartFraction pi Over 3 EndFraction
Step-by-step explanation:
we know that
The circumference of a circle subtends a central angle of 360 degrees or 2π radians
so
by proportion
Find out the central angle for an arc equal to One-sixth of the circumference of a circle
Let
x -----> the measure of the central angle in radians for an arc equal to One-sixth of the circumference
Simplify
therefore
StartFraction pi Over 3 EndFraction
Answer:
a)
b)
So the value of bread-making machine that separates the bottom 85% of data from the top 15% is 7.345.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Let X the random variable life of a bread making machine. We know from the problem that the distribution for the random variable X is given by:
We take a sample of n=9 . That represent the sample size.
From the central limit theorem we know that the distribution for the sample mean is also normal and is given by:
Solution to the problem
Part a
(a) the probability that the mean life of a random sample of 9 such machines falls between 6.4 and 7.2
In order to answer this question we can use the z score in order to find the probabilities, the formula given by:
The standard error is given by this formula:
We want this probability:
Part b
b) The value of x to the right of which 15% of the means computed from random samples of size 9 would fall.
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.85 of the area on the left and 0.15 of the area on the right it's z=1.036. On this case P(Z<1.036)=0.85 and P(Z>1.036)=0.15
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of bread-making machine that separates the bottom 85% of data from the top 15% is 7.345.
The question is missing the figure. So, the figure is attached below.
Answer:
C. 350 m
Step-by-step explanation:
Given:
Scale is given as:
1 unit : 25 meters
This means that 1 unit on the grid is equivalent to 25 meters in actual.
Now, from the figure, the horizontal distance across the park is 14 units.
1 unit = 25 meter
Now, we can find the actual distance using unitary method and thus multiplying 25 and 14 to get the actual distance across the park horizontally.
∴ 14 units = meters.
Therefore, the horizontal distance across the park is 350 m in actual.
So, the correct option is option C.
