Answer: 1/1000000000
Step-by-step explanation:
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Mean commute time (m) = 27.3 minutes
Standard deviation (sd) = 7.1 minutes
a) What minimum percentage of commuters in the city has a commute time within 2 standard deviations of the mean?
Using chebyshev's theorem ;
No more than 1/k² values of a distribution can be
k standard deviations from the mean.
Here k = 2
Hence,
1/k² = 1/2² = 1/4 = 0.25
Hence, minimum percentage of commmuters within 2 standard deviations of the mean :
1 - 0.25 = 0.75 m
B.) What minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the mean?
Here, k = 1.5
1/k² = 1/1.5² = 1/2.25 = 0.444
Hence, minimum commute time within 2 standard deviations of the mean :
1 - 0.444 = 0.56 = 56%
Commute time within 1.5 standard deviation
[27.3 - (1.5 × 7.1), 27.3 + (1.5 * 7.1)
[16.65, 37.95]
C.) What is the minimum percentage of commuters who have commute times between 6minutes and 48.6 minutes?
X - m /sd
X = 6
= (6 - 27.3) / 7.1 = - 3
X = 48.6
= (48.6 - 27.3) / 7. 1 = 3
Hence,
1/k² = 1 / 3² = 1/9
1 - 1/9 = 8/9
= 0.888 = 0.89 = 89%
The answers are choice A) and choice C). They effectively say the same thing but in a slightly different way. Choice A is more algebraic while choice C is more visual.
Answer:
8 and 3/10 < 8 and 7/10
Step-by-step explanation:
7/10 is more than 3/10
<h3>Answer: Approximately 191 bees</h3>
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Work Shown:
One way to express exponential form is to use
y = a*b^x
where 'a' is the initial value and 'b' is linked to the growth rate.
Since we're told 34 bees are there initially, we know a = 34.
Then after 4 days, we have 48 bees. So we can say,
y = a*b^x
y = 34*b^x
48 = 34*b^4
48/34 = b^4
24/17 = b^4
b^4 = 24/17
b = (24/17)^(1/4)
b = 1.090035
Which is approximate.
The function updates to
y = a*b^x
y = 34*(1.090035)^x
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As a way to check to see if we have the right function, plug in x = 0 and we find:
y = 34*(1.090035)^x
y = 34*(1.090035)^0
y = 34*(1)
y = 34
So there are 34 bees on day 0, ie the starting day.
Plug in x = 4
y = 34*(1.090035)^x
y = 34*(1.090035)^4
y = 34*1.4117629
y = 47.9999386
Due to rounding error we don't land on 48 exactly, but we can round to this value.
We see that after 4 days, there are 48 bees.
So we confirmed the correct exponential function.
------------------------
At this point we can find out how many bees there are expected to be after 20 days.
Plug in x = 20 to get
y = 34*(1.090035)^x
y = 34*(1.090035)^20
y = 190.672374978452
Round to the nearest whole number to get 191.
There are expected to be roughly 191 bees on day 20.
