Answer:
E(X) = 6
Var(X) = 3.394
Step-by-step explanation:
Let X represent the number of carp caught out of the 20 fishes caught. Now, if we are to assume that each
of the (100, 20) ways to catch the 20 fishes will be equally likely.
Thus, we can say that X fulfills a hypergeometric
distribution with parameters as follows;
n = 20, N = 100, k = 30
Formula for expected mean value in hypergeometric distribution is;
E(X) = nk/N
E(X) = (20 × 30)/100
E(X) = 6
Formula for variance is;
Var(X) = (nk/N) × [((n - 1)(k - 1)/(N-1))) + (1 - nk/N)]
Var(X) = ((20 × 30)/100) × [((20 - 1)(30 - 1)/(100 - 1)) + (1 - (20 × 30/100)]
Var(X) = 6 × 0.5657
Var(X) = 3.394
Answer:
Diana's score is better.
Step-by-step explanation:
In Diana case :
Score = 92
Mean score , μ = 71
Standard deviation σ = 15
So,
P( x ≥ 92 ) = 1 - P( x ≤ 92 )
= 1 - P(z ≤ )
= 1 - P( z ≤ )
= 1 - P( z ≤ 1.4 )
= 1 - 0.9192
= 0.0808 = 8.08 %
⇒P( x ≥ 92 ) = 8.08%
∴ we get
Diana score is > 91.92% other students in the class.
In Micheal case :
Score = 688
Mean score , μ = 493
Standard deviation σ = 150
So,
P( x ≥ 688 ) = 1 - P( x ≤ 688 )
= 1 - P(z ≤ )
= 1 - P( z ≤ )
= 1 - P( z ≤ 1.3 )
= 1 - 0.9032
= 0.0968 = 9.68 %
⇒P( x ≥ 688 ) = 9.68%
∴ we get
Micheal score is > 90.32% other students in the class.
From both scores , we can conclude that
Diana's score is better.
a) What is the ratio girls to boys in the class?
Answer: 2 : 1
b) What is the ratio boys to girls in the class?
Answer: 1 : 2
The first one is, as it equals x^2 -4^2
Answer:
Proportional: Mike, a plumber charges $5 per hour for his service.
Non-proportional: Mike charges a initial cost of $10 plus $3 for each hours of service.
Step-by-step explanation:
Let us assume that Mike, a plumber charges $5 per hour for his service.
So, the number of hours (h) of service and the total charge (C) are proportional, which is
C(h) = 5h ....... (1)
If the condition changes like, Mike charges an initial cost of $10 plus $3 for each hour of service.
Here, the equation that models the situation is
C(h) = 10 + 3h .......... (2)
Now, relation (1) is non-proportional. (Answer)