T probability of rolling doubles after 45 tosses is 0.156
How to determine the regression equation?
To do this, we enter the data values in a graphing calculator.
From graphing calculator, we have the following summary:
- Sum of X = 550
- Sum of Y = 87
- Mean X = 55
- Mean Y = 8.7
- Sum of squares (SSX) = 8250
- Sum of products (SP) = 1375
The regression equation is
y = bx + a
Where
b = SP/SSX = 1375/8250 = 0.16667
a = MY - bMX = 8.7 - (0.17*55) = -0.46667
So, we have:
y = 0.16667x - 0.46667
Approximate
y = 0.167x - 0.467
When the number of tosses is 45, we have:
y = 0.167 * 45 - 0.467
Evaluate
y = 7.048
Approximate
y = 7
45 tosses gives 7 doubles.
So, the probability is:
P = 7/45
Evaluate
P = 0.156
Hence, the probability of rolling doubles after 45 tosses is 0.156
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