Answer:
Prob = 0.00009 = 0.009% , Less Likely
Step-by-step explanation:
Using Binomial Distribution, Prob = N c r . ( P )^ r . ( Q ) ^ (n -r) .
,P = success probability, ie candidate considered be trustworthy = 70% = 0.7; N = trials = 200 ; Q = failure probability, ie non trustworthy = 1 - 0.7 = 0.3 r = no. of success = 116
Pr = 200c116 . (0.7)^116 . (0.3)^(200 - 116) = 200c116 (0.7)^116 (0.3)^84 = 0.00009 = 0.009%
Less probability means Less Likely
A) 5 to be chosen among a Total : 10 Men + 8 Women
¹⁸C₅ = (18!)/(5!)(13!) = 8,568 groups of five
b) A must to have men and women. If so we have to deduct all groups of 5 that are all men and all group of 5 that are all women
Groups of 5 with only men: ¹⁰C₅ = 252
Groups of 5 with only women: ⁸C₅ = 56
So number of committees of 5 men and women mixed =
8568 - 252 - 56 = 8,260 committees
c) 3 Women and 2 Men:
⁸C₃ x ¹⁰C₂ = 2,520 groups of 3 W and 2 M
d) More women than men, it means:
3 W + 2 M OR (we have found it in c) = 2,520)
4 W + 1 M OR ⁸C₄ x ¹⁰C₁ →→→→ = 700
5 W + 0 M OR ⁸C₅ x ¹⁰C₀ →→→→ = 56
Total where W>M = 3,276 groups of 5 where women are at least 3
In addition to mean and sample size you will need the individual scores.
The formula for standard deviation is:
S^2 = E(X-M)^2/N-1
Here's an example:
Data set: 4,4,3,1
Mean: 3
Sample size: 4
First, put the individual scores one after the other and subtract the mean from it.
4 - 3 = 1
4 - 3 = 1
3 - 3 = 0
1 - 3 = -2
Second, square the answers you got from step 1.
1^2 = 1
1^2 = 1
0^2 = 0
-2^2 = 4
Third, plug the values from step 2 into the formula.
S^2 = (1+1+0+4)/(4-1) = 6/3 = 2
Standard deviation = 2
1. 5.50 + 0.15 * 45 = 12.25
2. 4 + 0.20 * 45 = 13
So the first option is slightly better, you can save 13-12.25= $0.75.
The area of the garden would be 192 square feet. When you divide the area of his backyard by the side known, you find the missing side. The missing side is 24, which means that is the other leg of the triangle. By using the area formula for a right triangle you find the answer.