If a random variable X is exponentially distributed with parameter λ=2, then P(X≥1) is equal to
1 answer:
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Answer:
And using a calculator, excel ir the normal standard table we have that:
And we can calculate the probability like this:Step-by-step explanation:
A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the probability that the sample mean is in the interval 47<=X<53. Is the assumption of normality important. Why?
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 variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then we know that the distribution for the sample mean is given by:
We can find the probability required like this:
And using a calculator, excel ir the normal standard table we have that:
And we can calculate the probability like this:
Answer:
Peculiar purples would be more abundant
Step-by-step explanation:
Given that eculiar Purples and Outrageous Oranges are two different and unusual types of bacteria. Both types multiply through a mechanism in which each single bacterial cell splits into four. Time taken for one split is 12 m for I one and 10 minutes for 2nd
The function representing would be
i) for I bacteria where t is no of minutes from start.
ii) for II bacteria where t is no of minutes from start. P0 is the initial count of bacteria.
a) Here P0 =3, time t = 60 minutes.
i) I bacteria P =
ii) II bacteria P =
b) Since II is multiplying more we find that I type will be more abundant.
The difference in two hours would be
c) i) for I bacteria where t is no of minutes from start.
ii) for II bacteria where t is no of minutes from start. P0 is the initial count of bacteria.
d) At time 36 minutes we have t = 36
Peculiar purples would be
The rate may not be constant for a longer time. Hence this may not be accurate.
e) when splits into 2, we get
where P0 is initial and t = interval of time