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1 month ago

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Samir is an expert marksman. When he takes aim at a particular target on the shooting range, there is a 0.950.950, point, 95 pro

bability that he will hit it. One day, Samir decides to attempt to hit 101010 such targets in a row.

2 answers:

PIT_PIT [12.4K]1 month ago

6 0

The question appears to be incomplete. Here’s the complete inquiry:

Samir is quite skilled with the gun. When he targets a specific aim at the shooting range, he has a 0.95 probability of striking it. On one occasion, Samir sets out to shoot 10 targets consecutively.

If he has the same chance of hitting each of the 10 targets, what is the likelihood that he will miss at least one?

Response:

40.13%

Step-by-step breakdown:

Let 'A' represent the event of successfully hitting all targets in 10 trials.

The complement of 'A' is $\overline A=\textrm{Missing a target at least once}$

Now, since Samir has a consistent probability of hitting each target at 0.95.

Now, $P(A)=0.95^{10}=0.5987$

We know that the combined probability of an event and its complement equals 1.

<pThus, $P(A)+P(\overline A)=1\\\\P(\overline A)=1-P(A)\\\\P(\overline A)=1-0.5987\\\\P(\overline A)=0.4013=40.13\%$

Consequently, the probability that he misses at least one target among 10 attempts is 40.13%.

tester [12.3K]1 month ago

4 0

Response:

.401

Detailed explanation:

However, if rounding to the nearest tenth is required, then it would be.4.

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1. The following are the number of hours that 10 police officers have spent being trained in how to handle encounters with peopl

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Answer:

$Range = 16$

$Inter\ Quartile\ Range = 6.75$

$Variance = 20.44$

$Standard\ Deviation = 4.52$

Step-by-step explanation:

Provided

4, 17, 12, 9, 6, 10, 1, 5, 9, 3

Calculating the range;

$Range = Highest - Lowest$

From the data provided;

The highest value is 17 and the lowest is 1

Thus;

$Range = 17 - 1$

$Range = 16$

Calculating the inter-quartile range

The inter-quartile range (IQR) is computed as follows

$IQR = Q_3 - Q_1$

Where

Q3 = Upper Quartile and Q1 = Lower Quartile

Start by sorting the data in ascending order

1, 3, 4, 5, 6, 9, 9, 10, 12, 17

N = Total data points; N = 10

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Calculating Q3

$Q_3 = \frac{3}{4}(N+1) th\ item$

Substituting 10 for N

$Q_3 = \frac{3}{4}(10+1) th\ item$

$Q_3 = \frac{3}{4}(11) th\ item$

Expressing 8.25 as 8 + 0.25 $Q_3 = \frac{33}{4} th\ item$

$Q_3 = 8.25 th\ item$

Converting 0.25 into fractions

$Q_3 = (8 + 0.25) th\ item$

$Q_3 = 8th\ item + 0.25 th\ item$

From the ordered dataset;

$Q_3 = 8th\ item +\frac{1}{4} th\ item$ and

$Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)$

$8th\ item = 10$ $9th\ item = 12$

$Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)$

$Q_3 = 10 +\frac{1}{4} (12 - 10)$

$Q_3 = 10 +\frac{1}{4} (2)$

$Q_3 = 10 +0.5$

$Q_3 = 10.5$

Calculating Q1

Substituting 10 for N

$Q_1 = \frac{1}{4}(N+1) th\ item$

Expressing 2.75 as 2 + 0.75

$Q_1 = \frac{1}{4}(10+1) th\ item$

$Q_1 = \frac{1}{4}(11) th\ item$

$Q_1 = \frac{11}{4} th\ item$

$Q_1 = 2.75 th\ item$

Converting 0.75 into fractions

$Q_1 = (2 + 0.75) th\ item$

$Q_1 = 2nd\ item + 0.75 th\ item$

From the arranged dataset;

and $Q_1 = 2nd\ item +\frac{3}{4} th\ item$

$Q_1 = 2nd\ item +\frac{3}{4} (3rd\ item - 2nd\ item)$

$2nd\ item = 3$ $3rd\ item = 4$

$Q_1 = 3 +\frac{3}{4} (4 - 3)$

$Q_1 = 3 +\frac{3}{4} (1)$

$Q_1 = 3 +0.75$

$Q_1 = 3.75$

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Remember that

$IQR = Q_3 - Q_1$

$IQR = 10.5 - 3.75$

$IQR = 6.75$

Calculating Variance

Begin by determining the mean

$Mean = \frac{1+3+4+5+6+9+9+10+12+17}{10}$

$Mean = \frac{76}{10}$

$Mean = 7.6$

Then subtract the mean from each value and square the differences

$(1 - 7.6)^2 = (-6.6)^2 = 43.56$

$(3 - 7.6)^2 = (-4.6)^2 = 21.16$

$(4 - 7.6)^2 = (-3.6)^2 = 12.96$

$(5 - 7.6)^2 = (-2.6)^2 = 6.76$

$(6 - 7.6)^2 = (-1.6)^2 = 2.56$

$(9 - 7.6)^2 = (1.4)^2 = 1.96$

$(9 - 7.6)^2 = (1.4)^2 = 1.96$

$(10 - 7.6)^2 = (2.4)^2 = 5.76$

$(12 - 7.6)^2 = (4.4)^2 = 19.36$

$(17 - 7.6)^2 = (9.4)^2 = 88.36$

Sum up the squared results

$43.56 + 21.16 + 12.96 + 6.76 + 2.56 + 1.96 + 1.96 + 5.76 + 19.36 + 88.36 = 204.4$

Then divide that sum by the total number of observations;

$Variance = \frac{204.4}{10}$

$Variance = 20.44$

Calculating Standard Deviation (SD)

$SD = \sqrt{Variance}$

$SD = \sqrt{20.44}$

$SD = 4.52$ (Approximated)

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19 days ago

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tester [12383]

Answer:

40%

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John Smith and Susan Jones have contributed $240,000 and $160,000 respectively toward Expo Company. We are tasked with determining the proportion of the business owned by Susan.

First, calculate the total investment by summing both contributions.

$\text{Total money invested in business}=\$240,000+\$160,000$

$\text{Total money invested in business}=\$400,000$

Next, find what percentage $160,000 is of the total $400,000.

$\text{Percentage of business Susan own}=\frac{160,000}{400,000}\times 100$

$\text{Percentage of business Susan own}=0.4\times 100$

$\text{Percentage of business Susan own}=40$

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