Saguaro cacti are large cacti indigenous to thesouthwestern United States and Mexico. Assume that thenumber of saguaro cacti in
1 answer:
Answer:
Step-by-step explanation:
Given that Saguaro cacti are large cacti indigenous to thesouthwestern United States and Mexico. Assume that thenumber of saguaro cacti in a region follows a Poisson distribution with a mean of 280 per square kilometer.
a) Mean number of cacti per 10,000 square meters=280*10000 = 2800000
b) P(no cacti in 10000) sq m = P(X=0) for Poisson with parameter 2800000
= 0
(almost uncertain event)
c) Area of a region such that the probability of at least twocacti in the region is 0.9.
We get this is possible if mean = 8.4 for Poisson
i.e. region should have area as
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Answer:
And for this case we can use the complement rule and the normal standard distribution of excel and we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
And we select a sample size of n =70
From the central limit theorem (n>30)we know that the distribution for the sample mean is given by:
And we want to find this probability:
And we can use the z score formula given by:
And using this formula we got:
And for this case we can use the complement rule and the normal standard distribution of excel and we got: