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Svetlanka
2 months ago
9

According to a survey by Bankrate, of adults in the United States save nothing for retirement (CNBC website). Suppose that adult

s in the United States are selected randomly. a. Is the selection of the adults a binomial experiment? Explain. The selection - Select your answer - a binomial experiment because the adults are selected - Select your answer - , - Select your answer - from trial to trial, the trials - Select your answer - independent, and there are - Select your answer - outcomes possible. b. What is the probability that all of the selected adults save nothing for retirement (to 4 decimals)? c. What is the probability that exactly five of the selected adults save nothing for retirement (to 4 decimals)? d. What is the probability that at least one of the selected adults saves nothing for retirement (to 4 decimals)?
Mathematics
1 answer:
tester [12.3K]2 months ago
4 0

Complete Question

The complete question appears in the first uploaded image

Answer:

a) Yes, selecting 15 corresponds to a binomial experiment

b)

c)

d) P(r = 15) = 3.2768 *10^{-11}

Step-by-step explanation:

Regarding question a:

For an experiment to qualify as binomial

the trials have to be independent

each trial must yield one of two possible outcomes

Given that the selection of 15 individuals is random, we ascertain that the trials are independent and the outcomes are “either the individual saves for retirement or does not save for retirement.”

Therefore, we conclude that the selection of 15 people at random is indeed a binomial experiment.

In question b:

The probability that all selected adults do not save for retirement is mathematically modeled as

P(r = n) = ^nC_r * p^r * q^{n-r}

Here C signifies combination

r = 15 implies all selected adults

n refers to the population size equating to 15

From the problem, p = 0.20

and q can be calculated as

=>

=> q = 1 - p

Thus

P(r = 15) = ^{15}C_{15} * p^{15} * q^{15-15}

P(r = 15) = 3.2768 *10^{-11} Regarding question c:

The probability that exactly five of the selected adults do not save for retirement is mathematically modeled as

P(r = 5) = ^{15} C_5 * (0.20)^5 * (0.80)^{15}

P(r = 5) = 0.1032

In relation to question d:

The probability that at least one of the selected adults opts not to save for retirement can be mathematically expressed as

P(r \ge 1 ) = 1 - P (r = 0 )

P(r \ge 1 ) = 1 - [ ^{15} C _ 0 * (0.20)^{0} * (0.80 )^{15}]

P(r \ge 1 ) = 1 - 0.0352

P(r \ge 1 ) = 0.9648

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Response:

a. 55 cars

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Detailed explanation:

Let’s denote the quantity of cars with stereo systems as N(ss), those with air conditioning as N(ac), and those with sunroofs as N(sr).

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N(ss) = 30

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N(at least two) = 30

a.

To calculate how many cars possess at least one feature (N(at least one) or N(ss or ac or sr)), we apply:

N(ss or ac or sr) = N(ss) + N(ac) + N(sr) - N(ss and ac) - N(ss and sr) - N(ac and sr) + N(ss and ac and sr)

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Substituting, we find N(ss or ac or sr) = 30 + 30 + 40 - (30 + 2*15) + 15 = 55

b.

For those cars that have exactly one feature, we have:

N(only one) = N(at least one) - N(at least two)

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The length of a rectangle is measured as 370mm correct to 2 significant figures.
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Answer:

UB: 375

Step-by-step explanation:

370mm rounded to 2 significant figures is..

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If the area of the vegetable garden is 170 square feet which equation could be of use to find the length of the tomato patch? 0=
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Answer:

The equation 0 = 3x² + 17x - 160 might be useful in determining the length.

Step-by-step explanation:

The area of the vegetable garden is specified as 170 ft².

Now, regarding the provided equations;

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The square root value is negative, indicating no real solution for x.

Thus, this equation does not help find the length.

2) For the equation 0 = 3x² + 10x + 180, employing the quadratic formula, the square root value is also negative, hence there's no natural root for x. This means this equation can't be used to determine the length.

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4) For 0 = 3x² - 160, simplifying gives;

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Complete Question

The entire question can be found in the first uploaded image

Answer:

The expense for acquiring 100 shares of ODX group Inc and 300 shares of peer Comms Lts is

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Step-by-step explanation:

   From the chat, the expense for 100 shares of ODX is \$175

    The price of 100 shares of peer Comms Lts is \$ 200

Thus, the cost for 300 shares of peer Comms Lts amounts to k  =  3 * 200 =  \$ 600

Overall, the total cost for 100 shares of ODX group Inc and 300 shares of peer Comms Lts can be calculated as

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           C  =  \$ 775

 

 

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