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Luden [163]
2 years ago
11

1. A report from the Secretary of Health and Human Services stated that 70% of single-vehicle traffic fatalities that occur at n

ight on weekends involve an intoxicated driver. If a sample of 15 single-vehicle fatalities that occur on a weekend night is selected, find the probability that between 10 and 15, inclusive, accidents involved drivers who were intoxicated. (7 points)
Mathematics
1 answer:
Nuetrik [128]2 years ago
5 0

Using the binomial distribution, it is found that there is a 0.7215 = 72.15% probability that between 10 and 15, inclusive, accidents involved drivers who were intoxicated.

For each fatality, there are only two possible outcomes, either it involved an intoxicated driver, or it did not. The probability of a fatality involving an intoxicated driver is independent of any other fatality, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

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

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

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem:

  • 70% of fatalities involve an intoxicated driver, hence p = 0.7.
  • A sample of 15 fatalities is taken, hence n = 15.

The probability is:

P(10 \leq X \leq 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

Hence

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

P(X = 10) = C_{15,10}.(0.7)^{10}.(0.3)^{5} = 0.2061

P(X = 11) = C_{15,11}.(0.7)^{11}.(0.3)^{4} = 0.2186

P(X = 12) = C_{15,12}.(0.7)^{12}.(0.3)^{3} = 0.1700

P(X = 13) = C_{15,13}.(0.7)^{13}.(0.3)^{2} = 0.0916

P(X = 14) = C_{15,14}.(0.7)^{14}.(0.3)^{1} = 0.0305

P(X = 15) = C_{15,15}.(0.7)^{15}.(0.3)^{0} = 0.0047

Then:

P(10 \leq X \leq 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.2061 + 0.2186 + 0.1700 + 0.0916 + 0.0305 + 0.0047 = 0.7215

0.7215 = 72.15% probability that between 10 and 15, inclusive, accidents involved drivers who were intoxicated.

A similar problem is given at brainly.com/question/24863377

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Leviafan [203]

Answer:

Step-by-step explanation:

total: 200 employees of a company

119 had investments in stock funds

99 had investments in bond funds

65 had investments in money market funds

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33 had investments in bond funds and money market funds

21 had investments in stock funds, bond funds, and money market funds.

See Venn diagram attached

(a) What is the probability that an employee of the company chosen at random had investments in exactly two kinds of investment funds? (Enter your answer to three decimal places.)

Exactly 2 kinds: 26+12+12 = 50

50/200 = 0.25

(b) What is the probability that an employee of the company chosen at random had investments in exactly one kind of investment fund? (Enter your answer to two decimal places.)

Exactly one kind: 60+40+20 = 120

120/200 = 0.60

(c) What is the probability that an employee of the company chosen at random had no investment in any of the three types of funds? (Enter your answer to three decimal places.)

60+40+20+26+12+12+21=191

200-191 = 9

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8 0
3 years ago
Working alone, Jack can do a puzzle in 5 hours. With his brother's help, the two can do the same puzzle in 2 hours.
AysviL [449]

Answer:

3 hours and 20 minutes

Step-by-step explanation:

Jack's rate is 1 puzzle for every 5 hours, so his rate per hour is 1/5 of a puzzle per hour.

We need to find the rate of his brother so here is our equation,

1/5 + 1/x = 1/2

1/2 - 1/5 =1/x

3/10 = 1/x

3/ 3x = 3/10

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6 0
3 years ago
How much of the initial mass remains after 80 years? (Round your answer to three decimal places.)
aleksandr82 [10.1K]

Given

y=11(\frac{1}{2})^{\frac{t}{30}}

When t = 80

We substitute for t

y=11(\frac{1}{2})\frac{}{}^{\frac{80}{30}}

Simplify

y=11(\frac{1}{2})^{\frac{8}{3}}

Simplify further

y=1.732g

The final answer

4 0
1 year ago
a father is 24years older than his son. if the son is x years old, how old is the father and if the ratio of their ages is 5:2,
yan [13]

x+25/x=5/2

5x=2(x+24) 5x=2x+48

5x-2x=48

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the age of son=16

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6 0
3 years ago
Factors of 30 add up to 9. what are they?
Daniel [21]


1,2,3,5,6,10,15,30

think that's right, hope this helps!

8 0
3 years ago
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