A central angle θ in a circle of radius 4 m is subtended by an arc of length 5 m. find the measure of θ in degrees. (round your
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Answer:
a) 0.7291 is the probability that more than half out of 10 vehicles carry just 1 person.
b) 0.996 is the probability that more than half of the vehicles carry just one person.
Step-by-step explanation:
We are given the following information:
A) Binomial distribution
We treat vehicle on road with one passenger as a success.
P(success) = 64% = 0.64
Then the number of vehicles follows a binomial distribution, where
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 10
We have to evaluate:
0.7291 is the probability that more than half out of 10 vehicles carry just 1 person.
B) By normal approximation
Sample size, n = 92
p = 0.64
We have to evaluate the probability that more than 47 cars carry just one person.
After continuity correction, we will evaluate
Calculation the value from standard normal z table, we have,
0.996 is the probability that more than half out of 92 vehicles carry just one person.
Answer:
(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.
Step-by-step explanation:
Given that all the boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over.
This implies that boxes are in multiples of 12
i.e. 12, or 24, or 36 or....
Let us say this as 12m for m an integer
Now additional boxes arrived =60
Total number of boxes now =
This when arranged in stacks of 14,nothing left out
Or this is multiple of 14
for some positive integer n.
By trial and error we find that if 60 is to be divided by 14, 24 should be added and 24 is a multiple of 12.
So we say originally 24 boxes were there now 84 boxes there.
Hence both options are right.
(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.