Samantha has 4 1/2 gallons of lemonade for her daughter’s birthday party. Each gallon of lemonade contains 1.5 grams of fat. How
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Answer:
Choice C: approximately 121 green beans will be 13 centimeters or shorter.
Step-by-step explanation:
What's the probability that a green bean from this sale is shorter than 13 centimeters?
Let the length of a green bean be centimeters.
follows a normal distribution with
- mean
and
- standard deviation
.
In other words,
,
and the probability in question is .
Z-score table approach:
Find the z-score of this measurement:
. Closest to 0.86.
Look up the z-score in a table. Keep in mind that entries on a typical z-score table gives the probability of the left tail, which is the chance that will be less than or equal to the z-score in question. (In case the question is asking for the probability that
is greater than the z-score, subtract the value from table from 1.)
.
"Technology" Approach
Depending on the manufacturer, the steps generally include:
- Locate the cumulative probability function (cdf) for normal distributions.
- Enter the lower and upper bound. The lower bound shall be a very negative number such as
. For the upper bound, enter
- Enter the mean and standard deviation (or variance if required).
- Evaluate.
For example, on a Texas Instruments TI-84, evaluating gives
.
As a result,
.
Number of green beans that are shorter than 13 centimeters:
Assume that the length of green beans for sale are independent of each other. The probability that each green bean is shorter than 13 centimeters is constant. As a result, the number of green beans out of 150 that are shorter than 13 centimeters follow a binomial distribution.
- Number of trials
: 150.
- Probability of success
: 0.804317.
Let be the number of green beans out of this 150 that are shorter than 13 centimeters.
.
The expected value of a binomial random variable is the product of the number of trials and the probability of success on each trial. In other words,
The expected number of green beans out of this 150 that are shorter than 13 centimeters will thus be approximately 121.
Answer:
b. about 91.7 cm and 44.6 cm
Step-by-step explanation:
The lengths of the diagonals can be found using the Law of Cosines.
Consider the triangle(s) formed by a diagonal. The two given sides will form the other two sides of the triangle, and the corner angles of the parallelogram will be the measure of the angle between those sides (opposite the diagonal).
For diagonal "d" and sides "a" and "b" and corner angle D, we have ...
d² = a² +b² -2ab·cos(D)
The measure of angle D will either be the given 132°, or the supplement of that, 48°. We can use the fact that the cosines of an angle and its supplement are opposites. This means the diagonal measures will be ...
d² = 60² +40² -2·60·40·cos(D) ≈ 5200 ±4800(0.66913)
d² ≈ {1988.2, 8411.8}
d ≈ {44.6, 91.7} . . . . centimeters
The diagonals are about 91.7 cm and 44.6 cm.
