To work the problem out isolate k by subtracting 0.5 from both sides:
(k+0.5)-0.5=1.6-0.5
k=1.1
Hope i could help.
We calculate the z-score, by evaluating the z value of 0.96/2 = 0.48
The z-score for 0.48 = 2.054
Next, we multiply the z-score by the standard deviation.
i.e. 2.054 x 15 = 30.81
Next, we divide by the margin of error. (from the question, we want to estimate to within 3 minutes of the mean, thus our margin of error is 3.)
i.e. 30.81 / 3 = 10.27
Finally, we square the outcome,
i.e. 10.27^2 = 105.47
Therefore, to estimate within 3 minutes of the mean with 96% confidence, the researcher should take a minimum of 106 samples.
I don't think there's a way to find a form of a formula.
M<1+ m<2 = 90
-2x + 54 + 8x + 18 = 90
6x + 72 = 90
6x = 90 - 72
6x = 18
x = 3
m<1 = -2x + 54
m<1 = -2(3) + 54
m<1= -6 + 54
m<1 = 48