Sin angle that equals the 1/2 value is the 30 degree on the 1st Quadrant.
The angle of 30 degree on the 3rd Quadrant is equivalent to (formula and circle in the 1st photo) 180 + 30 = 210°.
So theta = 210° (3rd Quadrant) = 30° (1st Quadrant).
Now just transfer the cos 30° to the 3rd Quadrant and the signal will be negative (as shown in the 2nd photo attached).
Answer:
The standard deviation of weight for this species of cockroaches is 4.62.
Step-by-step explanation:
Given : A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams.
To find : What is the approximate standard deviation of weight for this species of cockroaches?
Solution :
We have given,
Mean
The sample mean x=55
A lab assistant reports that 14% of the cockroaches weigh more than 55 grams.
i.e. P(X>55)=14%=0.14
The total probability needs to sum up to 1,
The z-score value of 0.86 using z-score table is z=1.08.
Applying z-score formula,
Where, is standard deviation
Substitute the values,
The standard deviation of weight for this species of cockroaches is 4.62.