geno3141

a)  n = number in the batch, so n = 50

     p = probability of non-conformance = 5/50  =  1/10

b)  P(X≤2)  =  P(X=0) + P(X=1) + P(X=2)

                 =  50nCr0·(1/10)^0·(9/10)·50 + 50nCr1·(1/10)^1·(9/10)·49 + 50nCr2·(1/10)^2·(9/10)·48  

                  =  0.112

c)  P(X≥49)  =   P(X=49) + P(X=50)

                  =  50nCr49·(1/10)^49·(9/10)·1 + 50nCr50·(1/10)^50·(9/10)·0

                  =  $.51 x 10^-48

Let  L  represent the length of the longer leg.

Then  L - 8  represents the length of the shorter leg and  L + 8  represents the length of the longer leg.

Using the Pythagorean theorem:  (L)² + (L - 8)²  =  (L + 8)²

Multiplying out:                         L²  + L² - 16L + 64  =  L² + 16L + 64

Subtract 64 from both sides:      L²  + L² - 16L  =  L² + 16L

Subtract L² from both sides:      L² - 16L  =  16L

Subtract 16L from both sides:    L² - 32L  =  0

Factor:                                     L(L - 32)  =  0

Either     L = 0  (impossible)     or     L - 32  = 0     --->     L  =  32

If  L = 32,  then  L - 8  = 24     and     L + 8 = 40 

Let  L  represent length.

Let W  represent width.

Since the length is 6 yd longer than its width:  L  =  6 + W

The formula for perimeter:  P  =  2L + 2W   

Since the perimeter is 44 yds:     44  =  2L + 2W

Substituting:                             44  =  2(6 + W) + 2W

                                                44  =  12 + 2W + 2W

                                                44  =  12 + 4W

                                                32  =  4W

                                                 W  =  8 yds

Since  L  =  6 + W  --->  L  =  14 yds

Let L represent length     W represent width     and     A represent area.

Since the length is 3 ft more than twice the width, we can write this as     L = 3 + 2W

The formula for the area of a rectangle is     A = L x W

Since the area is 77,     77  =  L x W

Substituting:               77  =  (3 + 2W) x W

Multiplying out:           77  =  3W + 2W²

Rewriting:                  2W² + 3W  =  77

Subtracting:               2W² + 3W - 77  =  0

Factoring:                   (2W - 11)(W + 7)  =  0

So, either  2W - 11 = 0   --->  2W  =  11   --->   W = 5.5 ft

           or  W + 7  =  0   --->   W  =  -7    (not possible)

Since  L  =  3 + 2W   --->   L  =  3 + 2(5.5)  =  14 ft

Try Google, you can find a lot of things there ...

Poisson Distribution:  P(x, μ)  =  (e^-μ)(μ^x) / x!

Average number hitting the disk  =  0.1 x 100  =  10

With  μ - 10  and  x = 12:

      P(12, 10)  =  (e^-10)(10^12) / 12!   =   0.095  (approximately)

a)  The probability of randomly choosing someone with blood type O-negative is 12/200.

     The probability of randomly choosing someone without blood type O-negative is 188/200.

     The probability of randomly choosing three type-O and seventeen non-type-O is:

          (12/200)^3 x (188/200)^17 x the number of ways that this can occur.

     Since the order in which these are chosen is unimportant, it is a combination, so we been the combination of           choosing three out of twenty:  20nCr3

     Our probabiltiy has become:  20nCr3 x (12/200)^3 x (188/200)^17  =  0.086   (approx.)

b)  "At least one" means "one or more", so the easiest way is to find the probability that none have type O-              negative blood and subtract this from 1.000.

     The probability that none has type O-negative blood is:  20nCr0 x (12/200)^0 x (188/200)^20  =  0.290

     Subtracting this from 1.000 gives a probability of 0.710.

There are 6 · 6 outcomes for tossing two dice.

Of these ways there are 6 ways to get a sum of 7:  1&6, 2&5, 3&4, 4&3, 5&2, and 6&1.

There are 5 ways to get a sum of 6:  1&5, 2&4, 3&3, 4&2, and 5&1.

The probability of getting a 7 from a roll of two dice is 6/36.    (Let me call this outcome A.)

The probability of getting a 6 from a roll of two dice is 5/36.    (Let me call this outcome B.)

The probability of getting any other outcome is 25/36.            (Let me call this outcome X.)

The number of ways to arrange AABBXXXXXX is 10! / [ 2! · 2! · 6! ]  =  1260 ways 

So the probability is   1260 · (6/36)² · (5/36)² · (25/36)^6  =  0.0198 (approximately) 

Use the distributive property:

3(2 - 3x)     =     3(2) - (3)(3x)  =  6 - 9x