A biologist created the following graph to show the relationship between the temperature of water (x), in degrees Celsius, and t
he number of insect larvae (y) in the water: graph of y equals minus 2 times the square of x plus 20 times x plus 400 What does the peak of the graph represent?
2 answers:
Answer:
The maximum number of larvae occurs when the temperature is 5°C.
Step-by-step explanation:
We are given the function ,
where x= temperature of water (in degrees) and y= number of insect larvae in water.
From the graph of the function below, we see that,
The peak or the highest point of the parabola is (5,450).
That is, when x= 5, then the value of y= 450
<em>That is, when the temperature of the water is 5°, then the number of larvae in water is 450.</em>
Hence, the peak of the graph means that,
The maximum number of larvae occurs when the temperature is 5°C.
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Answer:
Mean: 0.9 pistons
Standard deviation: 0.944 pistons
Step-by-step explanation:
Either a piston is defective, or it is not. This means that for either piston, there can only be two outcomes. This means that we can solve this problem by the binomial distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and each trial can only have two outcomes, with probabilities and
.
For an experiment with n repeated trials and a probability of success , we have that:
The mean is:
The standard deviation is:
In this problem
There are 90 pistons, so .
There is a 1% probability that a piston is defective, so .
Estimate the number of pistons in the sample that are defective by giving the mean of the relevant distribution:
Quantify the uncertainty of your estimate by giving the standard deviation of the distribution.