Answer:
<h2>495 different ways</h2>
Step-by-step explanation:
We will use the combination rule to solve this questions since it bothers selection. Combination has to do with selection.
If r objects are to be selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
If there are Eight committee members meeting in a room that has twelve chairs, the number of ways they can sit in the chair can be done in 12C8 number of ways.
12C8 = 12!/(12-8)!8!
12C8 = 12!/4!8!
12C8 = 12*11*10*9*8!/4*3*2*8!
12C8 = 12*11*10*9/4*3*2
12C8 = 11*10*9/2
12C8 = 11*5*9
12C8 = 495
<em>Hence the committee can sit in the chairs in 495 different ways</em>
To answer this, set up a system of equations. What we know is that
5x + 2y = 100
And...
x+y=38
x represents the unknown number of 5 points questions
y represents the unknown number of 2 point questions
In my opinion the easiest way to solve this is to use substitution (that is when you find out the value of one variable, either x or y, and substitute that value as the variable).
So,
x+y=38
Subtract x from both sides
y=38-x
Now, plug (38-x) in as y in the other equation.
5x + 2(38-x) = 100
5x + 76-2x= 100
3x+76=100
3x=24
x=8
Now that you know that x=8, you can solve for y.
5x+2y=100
5(8)+2y=100
40+2y=100
2y=60
---- ------
2 2
y=30
X=8
Y=30
There are 8 five point questions on the test and 30 two point questions on the test
Answer:
0.78814
Step-by-step explanation:
We solve using z score
z = (x-μ)/σ, where
x is the raw score = 4.0 inches
μ is the population mean = 4.4 inches
σ is the population standard deviation = 0.5 inches
z = 4.0 - 4.4/0.5
z = -0.8
Probability value from Z-Table:
P(x<4.0) = 0.21186
P(x>4.0) = 1 - P(x<4.0)
= 1 - 2.1186
= 0.78814
The probability that the rod you chose will be greater than 4.0 inches is 0.78814.
Answer:
Step-by-step explanation:
The mean of the gas mileages is 317÷16=19.8125
317 is the sum total of all the figures and 16 is the number of figures in the distribution
Standard deviation is the square root of the variance and the variance is the mean of all squared deviations
The 16 squared deviations are
7.9102(×2) + 3.2852(×2) + 0.6602(×3) + 0.0352(×4) + 1.4102(×3) + 10.1602 + 17.5352 = 56.4382
56.4382÷16 = 3.5274
This is the Variance. The standard deviation is herefore √3.5274 =1.878 ~ 1.88 (to 2 decimal places)
(B) Chebyshev's inequality predicts that 75% of the selection will fall within 2 standard deviations of the mean
2×1.88=3.76
19.8125-3.76 = 16.05
19.8125+3.76= 23.57
The gas mileages are between 16.05 and 23.57
(C) the actual % of SUV models of the sample that fall in the above range is (15/16 × 100) = 93.75%
(D) the empirical rule gives the more accurate prediction
