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IgorLugansk [536]
3 years ago
9

The average number of field mice per acre in a 5-acre wheat field is estimated to be 12. find the probability that fewer than 7

field mice are found
Mathematics
1 answer:
zaharov [31]3 years ago
8 0
This requires the Poisson distribution, where
area = 5-acres
and mean number of field mice = 12 (in 5-acres of field)
therefore 
lambda=12 (mean, given)
and the probability of k mice in the 5-acre field is given by the Poisson distribution as
P(X=k)=lambda^k * e^(-lambda) / k!   ..............(1)
To find the probability of having LESS than 7 field mice, we add the probabilities of 0 to 6, which is
P(X<7)=P(X=0)+P(X=1)+...+P(X=6)
evaluating with equation (1) for X=0 to 6, we get:
0 0.0000061 0.0000742 0.0004423 0.0017704 0.0053095 0.0127416 0.025481Total = 0.045822

Answer: The probability that fewer than 7 field mice are found in the 5-acre field is 0.0458.
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Step-by-step explanation:

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3 years ago
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6 0
3 years ago
Simplify
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6 0
3 years ago
g In R simulate a sample of size 20 from a normal distribution with mean µ = 50 and standard deviation σ = 6. Hint: Use rnorm(20
Illusion [34]

Answer:

> a<-rnorm(20,50,6)

> a

[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905

[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501

Then we can find the mean and the standard deviation with the following formulas:

> mean(a)

[1] 50.72451

> sqrt(var(a))

[1] 7.470221

Step-by-step explanation:

For this case first we need to create the sample of size 20 for the following distribution:

X\sim N(\mu = 50, \sigma =6)

And we can use the following code: rnorm(20,50,6) and we got this output:

> a<-rnorm(20,50,6)

> a

[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905

[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501

Then we can find the mean and the standard deviation with the following formulas:

> mean(a)

[1] 50.72451

> sqrt(var(a))

[1] 7.470221

5 0
3 years ago
Which linear function represents the line given by the point-slope equation y – 8 = (x – 4)? f(x) = x + 4 f(x) = x + 6 f(x) = x
andrew11 [14]
It is understood without being written that the slope of this line is 1.  If we rewrite the point-slope form of the line it would be y-8=1(x-4) where 1 is the slope.  We move the -8 over by addition to get y = 1x-4+8, or, simplified, y=x+4, the first choice in your answers.
7 0
3 years ago
Read 2 more answers
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