Virginia is selling boxes of chocolates for a school fundraiser. She started to graph the relationship between the number of cho
colates below.
According to the graph, how many chocolates are in 3 boxes?
OA. 10
OB. 12
OC. 15
OD. 16
According to the graph, how many chocolates are in 3 boxes?
OA. 10
OB. 12
OC. 15
OD. 16
2 answers:
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Answer:
a) P ( X = 2 ) = 0.23028
b) P ( X < 4 ) = 0.95689
c) P ( X ≥ 3 | X ≥ 2 ) = 0.38292
Step-by-step explanation:
Given:-
- The parameter for the poisson distribution is given, λ = 1.3.
- Declare a random variable (X) which is the number of books sold in the next minute:
X ~ Po (1.3)
Find:-
a) What's the probability that the store will sell 2 books in the next minute? b) What's the probability that the store will sell less than 4 books in the next minute? c) What's the probability that the store will sell at least 3 books in the next minute given that it sells at least 2 books in the next minute?
Solution:-
a) The required probability P ( X = 2 ). Can be computed by using the pmf for the poisson distribution:
Where, "k" is the number of books sold in next minute.
- Now compute P ( X = 2 ) :
b) The required probability P ( X < 4 ). Can be computed by using the pmf for the poisson distribution and summing individual terms from 0 - 3:
c) The required probability P ( X ≥ 3 | X ≥ 2 ). We have to consider the conditional probability as follows:
P ( X ≥ 3 | X ≥ 2 ) = P ( X ≥ 3 & X ≥ 2 ) / P (X ≥ 2 )
= P ( X ≥ 3 ) / P (X ≥ 2 )
= P ( X > 2 ) / P ( X > 1 )
= [ 1 - P ( X ≤ 2 ) ] / [ 1 - P ( X ≤ 1 ) ]
- Compute P ( X ≤ 2 ) & P ( X ≤ 1 ) using pmf:
P ( X ≤ 2 ) = 0.27253 + 0.35429 + 0.23028
= 0.8571
P ( X ≤ 1 ) = 0.27253 + 0.35429
= 0.62682
- Use the expression developed for conditional probability to evaluate the required probability:
P ( X ≥ 3 | X ≥ 2 ) = [ 1 - P ( X ≤ 2 ) ] / [ 1 - P ( X ≤ 1 ) ]
= [ 1 - 0.8571 ] / [ 1 - 0.62682 ]
= 0.38292
The values would be
sin2x = -3/5
cos2x = -4/5
tan2x = 3/4
What are double angles in trigonometry?
The double angle formulas are used to find the values of double angles of trigonometric functions using their single angle values. For example, the value of cos 30° can be used to find the value of cos 60°. Also, the double-angle formulas can be used to derive the triple-angle formulas.
Given: tanx = -3
Now as we know,
Now
And similarly, we can find the value of tan2x, as
tan2x = sin2x/cos2x
= (-3/5)/(-4/5)
= 3/4
Hence,
The values would be
sin2x = -3/5
cos2x = -4/5
tan2x = 3/4
To learn more about double angles in trigonometry, visit:
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