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Kobotan [32]
3 years ago
15

A​ four-year study of various brands of bottled water found that 25​% of bottled water is just tap water packaged in a bottle. C

onsider a sample of sevenseven ​bottled-water brands, and let x equal the number of these brands that use tap water. Complete parts a through d.
a. Is x​ (approximately) a binomial random​ variable?
b. Give the probability distribution for x as a formula.
c. Find p(x = 2).
d. Find P(x <= 1).
Mathematics
1 answer:
finlep [7]3 years ago
8 0

Answer:

Answers below

Step-by-step explanation:

a. Is x​ (approximately) a binomial random​ variable?

b. Give the probability distribution for x as a formula.

c. Find p(x = 2).

d. Find P(x <= 1).

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The sum of 2 consecutive numbers is 69. What are the numbers?
Vaselesa [24]

Answer:

<h3>            34, 35</h3>

Step-by-step explanation:

z - some integer

then the consecutive integer would be:

z+1,  (or z-1)

the sum is 69 so:

z + z+1 = 96

2z = 68

z = 34

z+1 = 34 + 1 = 35

(or:

z + z-1 = 69

2z = 70

z = 35

z-1 = 35 - 1 = 34)

7 0
3 years ago
The ordered pair R(-2, 7) is translated 5 units to the right and 2 units down.
Usimov [2.4K]
Left and right affect domain. (x)

Up and down effects range. (y)

So,

-2+5 (because the right of the number line is an increase)

7-2 (because you are decreasing by going down)

You are left with:

R'(3,5)

I hope this helps!
~cupcake
8 0
3 years ago
Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal prob
Novay_Z [31]

Answer:

a) By the Central Limit Theorem, it is approximately normal.

b) The standard error of the distribution of the sample mean is 1.8333.

c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours

e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 36 hours and a standard deviation of 5.5 hours.

This means that \mu = 36, \sigma = 5.5

a. What can you say about the shape of the distribution of the sample mean?

By the Central Limit Theorem, it is approximately normal.

b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

Sample of 9 means that n = 9. So

s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333

The standard error of the distribution of the sample mean is 1.8333.

c. What proportion of the samples will have a mean useful life of more than 38 hours?

This is 1 subtracted by the pvalue of Z when X = 38. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{38 - 36}{1.8333}

Z = 1.09

Z = 1.09 has a pvalue of 0.8621

1 - 0.8621 = 0.1379

0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d. What proportion of the sample will have a mean useful life greater than 34.5 hours?

This is 1 subtracted by the pvalue of Z when X = 34.5. So

Z = \frac{X - \mu}{s}

Z = \frac{34.5 - 36}{1.8333}

Z = -0.82

Z = -0.82 has a pvalue of 0.2061.

1 - 0.2061 = 0.7939

0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.

e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?

pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So

0.8621 - 0.2061 = 0.656

0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

4 0
3 years ago
17. You roll a number cube. How likely is it that you will roll a number less than 7? <br> Explain
Lyrx [107]

Answer:

1 or 100%.

Step-by-step explanation:

The probability of rolling less than 7 is equal to the probability of rolling 1 or 2 or 3 or 4 or 5 or 6. That is 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6. So any number from the dice can come up when you roll it because a perfect dice has 6 sides.

6 0
1 year ago
Determine the solution of the system. Show your work
Oxana [17]
First question:

1. Set equations equal to each other so 5x-9=2x+6
2. Put x's on one side so that 3x=15
3. Divide by 3 so that x=15
4. Substitute 15 in for x so that y=2(15)+6
5. Solve for y so that y=36
6. Thus the equations intersect at (15,36)

Second question:

1. Since for lines y=mx+b, and m=slope=3 you only need to write an equation with slope 3
2. y=3x+b, b can be any number
3 0
2 years ago
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