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adelina 88 [10]
3 years ago
12

If there are 1500 guests, only 1 of them brought a coupon for free admission to the carnival?

Mathematics
1 answer:
wlad13 [49]3 years ago
4 0
So 1/50 brought the pass
x out 1500
1/50 = x/1500
cross multiply
1500 = 50x
divide both sides by 50
30 = x

You can expect for 30 out of the 1,500 to receive free admissions. 

Hope this helps 
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Two opposing opinions were shown to a random sample of 1,500 buyers of a particular political news app in the United States. The
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Answer:

A) 98% Confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B

= (0.51, 0.57)

This means that the true proportion of all thay would chose opinion B can take on values between the range of (0.51, 0.57)

B) For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion of all US buyers of this particular app who would have chosen Opinion B = 0.54

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 98% confidence interval for sample size of 1500 is obtained from the z-tables.

Critical value = 2.33

Standard error = σₓ = √[p(1-p)/n]

p = sample proportion = 0.54

n = sample size = 1500

σₓ = √(0.54×0.46/1500) = 0.0128685664 = 0.01287

98% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.54 ± (2.33 × 0.01287)

CI = 0.54 ± 0.02998)

98% CI = (0.51, 0.57)

98% Confidence interval = (0.51, 0.57)

B) The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?

For this confidence interval to be obtained using sample data, a couple of conditions are necessary to be satisfied. They include;

- The sample data must have been obtained using a random sampling technique.

- The sampling distribution must be normal or approximately normal.

- The variables of the sample data must be independent of each other.

On the second point, the condition for a binomial distribution to approximate a normal distribution is that

np ≥ 10

and n(1-p) ≥ 10

The quantity np is the actual sample mean which is the actual number of buyers that chose Opinion B while n(1-p) is the number of buyers that did not chose Opinion B.

For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Hope this Helps!!!

8 0
3 years ago
When Samuel commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 32 minutes and a
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Answer:

z=\frac{x-\mu}{\sigma}

And we can find the nnumber of deviations from the mean for each limit given:

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So we are 3 deviation from the mean and using the empirical rule we know that within 3 deviations from the mean we have 99.7% of the values

Step-by-step explanation:

Let X the random variable that represent the amount of time it takes him to arrive, and for this case we know the distribution for X is given by:

X \sim N(32,5)  

Where \mu=32 and \sigma=5

We want to find this probability:

P(17

And we can use the z score formula given by:

z=\frac{x-\mu}{\sigma}

And we can find the nnumber of deviations from the mean for each limit given:

z_1 = \frac{17-32}{5} = -3

z_2= \frac{47-32}{5} = 3

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8 0
3 years ago
The ratio of the measures of the sides of a triangle is
Liono4ka [1.6K]

Answer:

X = 48 inches  for the shortest side

Step-by-step explanation:

9s = first side

10s = second side

4s = third side

Perimeter = sum of the sides

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     12 = s

9s = first side;  9(12) = 108

10s = second side;  10(12) = 120

4s = third side; 4(12) = 48  

3 0
3 years ago
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