How do you find the area of a 2x-3 square
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Answer:
a. P(24)=0.00007
b. P(23)=0.00018
c. There is significant difference between the probability of the rainy days and the probabilities of fire and theft.
The probability of theft would be overestimated by 76% and the probability of fire would be subestimated by 27%.
Step-by-step explanation:
The probabilities of two events ("fire"and "theft") are compared to the probabilities of a certain number of days of rain during July.
The probabilities of "fire"and "theft" are around P=0.0001, and we need to calculate if the probability of exactly 23 and exactly 24 days of rain July have approximately the same probability.
Rain frequencies for the months of July and August were shown to follow a Poisson distribution with a mean of 10 days per month.
The parameter then is:
The probability of k days of rain is:
For 24 days, the probability is:
The probability of 23 days of rain is 27% less than P=0.0001.
For 23 days of rain, the probability is:
The probability of 23 days of rain is 76% more than P=0.0001.
There is significant difference between the probability of the rainy days and the probabilities of fire and theft.
The probability of theft would be overestimated by 76% and the probability of fire would be subestimated by 27%.
Answer:
c. A and C
Step-by-step explanation:
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
We need to check the conditions in order to use the normal approximation.
So we see that we satisfy the conditions and then we can apply the approximation.
If we appply the approximation the new mean and standard deviation are:
Part A
We want this probability:
The z score is defined as
.
Part B
P(X>12) = 1-P(X\leq 12) = 1-P(Z< \frac{12-11}{3.129})=1-0.625=0.375[/tex]
Part C
The z score is defined as
.
So then the best option is : c. A and C