Help needed for some geometry
2 answers:
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Answer:
99.87% of cans have less than 362 grams of lemonade mix
Step-by-step explanation:
Let the the random variable X denote the amounts of lemonade mix in cans of lemonade mix . The X is normally distributed with a mean of 350 and a standard deviation of 4. We are required to determine the percent of cans that have less than 362 grams of lemonade mix;
We first determine the probability that the amounts of lemonade mix in a can is less than 362 grams;
Pr(X<362)
We calculate the z-score by standardizing the random variable X;
Pr(X<362) =
This probability is equivalent to the area to the left of 3 in a standard normal curve. From the standard normal tables;
Pr(Z<3) = 0.9987
Therefore, 99.87% of cans have less than 362 grams of lemonade mix
Though you do not provide a diagram, I am going to give this a try by assuming that O is the center of the circle, OA is a radius, and angle AOB is a central angle that measures 88 degrees.
We want to find out the area of sector AOB. First, we need to find the area of the entire circle. The area of a circle is given by
and since the radius of this circle is equal to 1, the area is 
Next we need to know what fraction of the circle sector AOB represents. The distance around the circle is 360 degrees but the central angle that intercepts arc AB is 88 degrees. That meas that the fraction of the circle the sector represents is given by
We multiply this by the area to obtain
which is the area of the sector.
We want to find out the area of sector AOB. First, we need to find the area of the entire circle. The area of a circle is given by
Next we need to know what fraction of the circle sector AOB represents. The distance around the circle is 360 degrees but the central angle that intercepts arc AB is 88 degrees. That meas that the fraction of the circle the sector represents is given by
We multiply this by the area to obtain