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2 years ago

3. The probability of a marksman scoring a bulls-eye on any shot is 0.26. The probability

Mathematics

1 answer:

Misha Larkins [42]2 years ago

8 0

Answer:

a) 0.68

b) 0.08

c) 0.74

Step-by-step explanation:

Given that:

Probability of hitting bulls eye, P(B) = 0.26

Probability of an inner, P(I) = 0.42

Probability of an outer, P(O) = 0.24

a) Probability of hitting an inner or better (inner or bulls eye):

P(I or B) = P(I $\cup$ B)

Formula for P(P $\cup$ Q) where P(P) and P(Q) are the probabilities of two mutually exclusive events i.e. having nothing in common:

P(P $\cup$ Q) = P(P) + P(Q)

P(I $\cup$ B) = P(I) + P(B) = 0.26 + 0.42 = 0.68

b) Probability of failing to hit the target:

P(F) = 1 - (P(B)+P(I)+P(O))

P(F) = 1 - (0.26 + 0.42 + 0.24)) = 1 - 0.92 = 0.08

c) Probability of failing to score a bulls eye:

P(B)' = 1 - P(B) = 1 - 0.26 = 0.74

So, the answers are:

a) 0.68

b) 0.08

c) 0.74

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The probabilities of the orphaned pets in six cities' animal shelters being different types of animals are given in the table. I

olga2289 [7]

Given the table below showing the probabilities of the orphaned pets in six cities' animal shelters being different types of animals.


 City Cat Dog Dog Dog Dog
 −Lhasa Apso −Mastiff −Chihuahua −Collie
Austin 24.5% 2.76% 2.86% 3.44% 2.65%
Baltimore 19.9% 3.37% 3.22% 3.31% 2.85%
Charlotte 33.7% 3.25% 3.17% 2.89% 3.33%
St. Louis 43.8% 2.65% 2.46% 3.67% 2.91%
Salt Lake
City 28.9% 2.85% 2.78% 2.96% 2.46%
Orlando 37.6% 3.33% 3.41% 3.45% 2.78%
Total 22.9% 2.91% 2.68% 3.09% 2.58%

Condtional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B).

The probability of A given B, is given by
$P(A|B)= \frac{P(A\cap B)}{P(B)}$

From the table, the probability that an orphaned pet in a St. Louis animal shelter is a mastiff dog is 2.46% and the probability that an orphaned pet in a St. Louis animal shelter is a dog is 2.91% + 2.68% + 3.09% + 2.58% = 11.26%

The probability that a randomly selected orphaned pet in a St. Louis animal shelter is a mastiff given that it is a dog, is given by
$\frac{P(St. \, Louis\, and\, dog-mastiff)}{P(dog)} = \frac{2.46}{11.26} \times100\%=21.85\%$

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2 years ago

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Is the statement "Two matrices are row equivalent if they have the same number of rows" true or false? Explain. A. True, because

vlabodo [156]

Answer: The answer is (C).

Step-by-step explanation: The given statement is - "Two matrices are row equivalent if they have the same number of rows". We are to explain whether the statement is true or false.

What are row equivalent matrices? The answer to this question is -

Two matrices are said to be row equivalent if one of the matrices can be obtained from the other by applying a number of elementary row operations. Or, we can say two matrices of same order are row equivalent if they have same row space.

Thus, the correct option is (C).

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2 years ago

The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for

saul85 [17]

Answer:

y hat = 2114.20 + 18.96x

Step-by-step explanation:

Given the least square regression model equation:

y hat = -959.00 + 8.60x

weld diameter x ; shear strength y (in pounds)

1 lb = 0.4536 kg

To express shear strength y in kilogram:

y is multiplied by 0.4536

(y hat × 0.4536) = -959.00 + 8.60x

Divide both sides by 0.4536

(y hat × 0.4536) / 0.4536= (-959.00 + 8.60x) / 0.4536

y hat = 2114.1975 + 18.959435x

y hat = 2114.20 + 18.96x

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2 years ago

Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numb

dezoksy [38]

Answer:

The calculated value Z = 3.775 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The Two Population proportion are not equal

Step-by-step explanation:

Given first sample size n₁ = 677

First sample proportion

$p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{172}{677} = 0.254$

Given second sample size n₂ = 3377

second sample proportion

$p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{654}{3377} = 0.1936$

Null Hypothesis : H₀ : p₁ = p₂.

Alternative Hypothesis : H₁ : p₁ ≠ p₂.

Test statistic

$Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{P Q(\frac{1}{n_{1} } +\frac{1}{n_{2} }) } }$

where

$P = \frac{n_{1} p_{1} + n_{2} p_{2} }{n_{1}+n_{2} } = \frac{677 X 0.254+3377 X 0.1936}{677+3377}$

P = 0.2036

Q = 1 - P = 1 - 0.2036 = 0.7964

$Z = \frac{0.254- 0.1936 }{\sqrt{0.2036 X 0.7964(\frac{1}{677 } +\frac{1}{3377 }) } }$

Z = 3.775

Critical value ∝=0.05

Z- value = 1.96

The calculated value Z = 3.775 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The Two Population proportion are not equal

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2 years ago

an auto transport truck holds 12 cars. A car dealer plans to bring in 1006 new cars in June and July. if an auto transport truck

allochka39001 [22]

divide 1006 by 12

1006 / 12 = 83.833

so 83 full trucks

83 *12 = 996

1006-996 = 10 cars will be on the last truck

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2 years ago

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