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pishuonlain [190]
2 years ago
11

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.
Assuming that Samir is equally likely to hit each of the 101010 targets, what is the probability that he will miss at least one of them?
Round your answer to the nearest tenth.
Mathematics
1 answer:
Vinvika [58]2 years ago
7 0

Answer:

40.1% probability that he will miss at least one of them

Step-by-step explanation:

For each target, there are only two possible outcomes. Either he hits it, or he does not. The probability of hitting a target is independent of other targets. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

0.95 probaiblity of hitting a target

This means that p = 0.95

10 targets

This means that n = 10

What is the probability that he will miss at least one of them?

Either he hits all the targets, or he misses at least one of them. The sum of the probabilities of these events is decimal 1. So

P(X = 10) + P(X < 10) = 1

We want P(X < 10). So

P(X < 10) = 1 - P(X = 10)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 10) = C_{10,10}.(0.95)^{10}.(0.05)^{0} = 0.5987

P(X < 10) = 1 - P(X = 10) = 1 - 0.5987 = 0.401

40.1% probability that he will miss at least one of them

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Black_prince [1.1K]

Answer: FALSE.

Step-by-step explanation:

Given the following equation provided in the exercise:

x-13=x+1

You need to solve for the variable "x".

In order to solve for "x" you can folllow the steps shown below:

1. You must apply the Addition property of equality and add 13 to both sides of the equation. Then:

x-13+(13)=x+1+(13)\\\\x=x+14

2. Finally you need to apply the Subtraction property of equality and subtract "x" from both sides of the equation. So you get:

x-(x)=x+14-(x)\\\\0=14\ (FALSE)

Therefore, as you can observe, the given equation has no solutions.

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3 years ago
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2 years ago
Past experience has indicated that the breaking strength of yarn used in manufacturing drapery material is normally distributed
vlabodo [156]

Answer:

95% two-sided confidence interval on the true mean breaking strength is (94.8cm, 99.2cm)

Step-by-step explanation:

Our sample size is 11.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

df = 11-1 = 10.

Then, we need to subtract one by the confidence level \alpha and divide by 2. So:

\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 10 and 0.025 in the two-sided t-distribution table, we have T = 1.812

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

s = \frac{4}{\sqrt{11}} = 1.2060

Now, we multiply T and s

M = Ts = 1.812*1.2060 = 2.19/tex]For the lower end of the interval, we subtract the sample mean by M. So the lower end of the interval here is[tex]L = 97 - 2.19 = 94.81 = 94.8cm

For the upper end of the interval, we add the sample mean and M. So the upper end of the interval here is

L = 97 + 2.19 = 99.19 = 99.2cm

So

95% two-sided confidence interval on the true mean breaking strength is (94.8cm, 99.2cm).

7 0
3 years ago
Which is the better buy? 5-pack of toaster pastries for $4.13 or 9-pack of toaster pastries for $7.56
kolbaska11 [484]

Answer: <em>The answer is </em><u><em>9-pack of toaster pastries for $7.56</em></u>

Step-by-step explanation:

<em>Basicly it would be more expensive if you bought 9 for the first option but less for the other.</em>

5 0
2 years ago
Help? Thanks!!!!!!!! If possible show work please!
FrozenT [24]

Answer:

B =102

Y = 32

Step-by-step explanation:

Solving (47):

To solve for B, we have:

B + 50 + 28 = 180 --- sum of angles in a triangle

This gives

B + 78 = 180

Collect like terms

B =- 78 + 180

B =102

Solving (48):

To solve for Y, we have:

X + Y+ Z = 180 --- sum of angles in a triangle

This gives

Y = 180 - X - Z

Where

W+ X=180 -- angle on a straight line

Solve for X

X=180 -W

X=180 -100 = 80

So, we have:

Y = 180 - X - Z

Y = 180 - 80 - 68

Y = 32

5 0
3 years ago
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