MATHEMATICS COLLEGE

In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution with a mean of 0.62.(a) What is the probability of more than one death in a corps in a year?

(b) What is the probability of no deaths in a corps over 7 years?

Round your answers to four decimal places (e.g. 98.7654).

Answers

Answer 1
Answer:

Answer:

(a) The probability of more than one death in a corps in a year is 0.1252.

(b) The probability of no deaths in a corps over 7 years is 0.0130.

Step-by-step explanation:

Let X = number of soldiers killed by horse kicks in 1 year.

The random variable X\sim Poisson(\lambda = 0.62).

The probability function of a Poisson distribution is:

P(X=x)=(e^(-\lambda)\lambda^(x))/(x!);\ x=0,1,2,...

(a)

Compute the probability of more than one death in a corps in a year as follows:

P (X > 1) = 1 - P (X ≤ 1)

             = 1 - P (X = 0) - P (X = 1)

             =1-(e^(-0.62)(0.62)^(0))/(0!)-(e^(-0.62)(0.62)^(1))/(1!)\n=1-0.54335-0.33144\n=0.12521\n\approx0.1252

Thus, the probability of more than one death in a corps in a year is 0.1252.

(b)

The average deaths over 7 year period is: \lambda=7*0.62=4.34

Compute the probability of no deaths in a corps over 7 years as follows:

P(X=0)=(e^(-4.34)(4.34)^(0))/(0!)=0.01304\approx0.0130

Thus, the probability of no deaths in a corps over 7 years is 0.0130.

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A television is 28.5 inches wide and 16 inches long.Using the Pythagorean Theorem, what is the length of the diagonal of the television, rounded to the nearest inch?

Answers

Answer:

  33 in

Step-by-step explanation:

The Pythagorean theorem tells you ...

  diagonal² = length² +width²

  diagonal² = (16 in)² +(28.5 in)² = 1068.25 in²

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Mike buys a pack of markers for $2.85. He uses a 20% off coupon, what is the price of the markers with the coupon?A $2.28
B $3.42
C .57
D $2.53

Answers

The answer would be C

Answer:

c.57

Step-by-step explanation:

Jenny is either a hippie or an artist. But Jenny is certainly not a hippie. So it can be concluded that Jenny is an artist.

Answers

Answer:Yes

Step-by-step explanation:

In the question it is given that jenny is either a hippie or an artist .so there are two possibilities for jenny .

Further it is given that jenny is certainly not a hippie therefore one possibility is ruled out of being a hippie so we left with only one i.e. jennny being a artist.

So we can conclude that jenny is an artist

Answer:

yes

Step-by-step explanation:

there is only 1 reasonable answer.

A calzone is divided into 24 equal pieces. Sophie and Glenn each ate one-fourthof the calzone on Saturday. The next​ day, Glenn ate one-sixth
of the calzone that was leftover. How many of the pieces of the original calzone ​remain? Explain your reasoning.

Answers

Answer:

10 pieces

Step-by-step explanation:

Total no. of pieces of calzone = 24

No of pieces of calzone eaten by sophie = 1/4 of Total no. of pieces of calzone  = 1/4 of 24 = (1/4)*24= 6 pieces.

No of pieces of calzone eaten by Glenn = 1/4 of Total no. of pieces of calzone  = 1/4 of 24 = (1/4)*24= 6 pieces.

Total no of pieces eaten by both of them on saturday = 12.

No of pieces of calzone left = 24-12 = 12

_______________________________________________

No of pieces of calzone eaten by Glenn on next day = 1/6 of Total no. of pieces of calzone  left= 1/6 of 12 = (1/6)*12= 2 pieces

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Kurt's truck uses 10 gallons of gas to travel 140miles. He has 5 gallons in the tank. How much more gas will he need to drive 322 miles

Answers

Answer:

18 gallons

Step-by-step explanation:

Step 1:

140 : 10 = x : 5      Equation / Ratio

Step 2:

10x = 700     Multiply

Step 3:

x = 70     Divide

Step 4:

322 miles - 70 miles     To find how many miles are needed to get to 322

Step 5:

252 miles ÷ 14        To find the amount of gas  / Divide

Answer:

18 gallons more

Hope This Helps :)

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Answers

Answer:

60

Step-by-step explanation:
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