the number of mosquito at the beginning of the summer was 4,000. the population of mosquito is expected to grow at a rate of 25%
1 answer:
Answer:
<em>about 9765 mosquitoes</em>
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Step-by-step explanation:
This is an exponential growth problem which follows the formula:
Where A is the future amount (we need this after 4 months)
P is the initial amount (here, it is 4000)
r is the rate of increase (here it is 25% or 0.25)
t is the time period (here t= 4, because we want to know after 4 months)
<em>plugging in all the available/given info, we can solve for A:</em>
<em></em>
<em />
<em>Since, no fractional mosquitoes, we round down to </em><em>9765 mosquitoes</em>
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Answer:
a) A sample of 256 was used in this survey.
b) 45.14% probability that the point estimate was within ±15 of the population mean
Step-by-step explanation:
This question is solved using the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
a. How large was the sample used in this survey?
We have that . We want to find n, so:
A sample of 256 was used in this survey.
b. What is the probability that the point estimate was within ±15 of the population mean?
15 is the bounds with want, 25 is the standard error. So
Z = 15/25 = 0.6 has a pvalue of 0.7257
Z = -15/25 = -0.6 has a pvalue of 0.2743
0.7257 - 0.2743 = 0.4514
45.14% probability that the point estimate was within ±15 of the population mean
Answer: Second option.
Step-by-step explanation:
You need to use the following formula:
Where "B" is the area of its base and "h" is the height.
According to the data given in the exercise, you know that:
Therefore, knowing this values, you can substitute them into the formula shown before and then evaluate, in order to calculate the volume of thi right pyramid whose base is a regular hexagon.
Then, you get: