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motikmotik
2 years ago
14

The mayor of a city believes a large park in the city is becoming more popular and wants to expand nature programs at the park.

A random sample of 30 summer days are selected and the number of park visitors is determined for each of those days. From this sample, the mean number of visitors was X(xbar) = 98.3 with a standard deviation of Sx = 11.2. Calculate a 99% confidence interval for the true mean number of visitors on summer days. Assume the conditions for inference are met.
a. 95.192 to 101.410 visitors
b. 34.123 to 162.480 visitors
c. 92.664 to 103.940 visitors
d. None of these is correct.
Mathematics
1 answer:
mariarad [96]2 years ago
8 0

Using the t-distribution, as we have the standard deviation for the sample, it is found that the 99% confidence interval for the true mean number of visitors on summer days is given by:

c. 92.664 to 103.940 visitors

<h3>What is a t-distribution confidence interval?</h3>

The confidence interval is:

\overline{x} \pm t\frac{s}{\sqrt{n}}

In which:

  • \overline{x} is the sample mean.
  • t is the critical value.
  • n is the sample size.
  • s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a<u> two-tailed 99% confidence interval</u>, with 30 - 1 = <em>29 df</em>, is t = 2.756.

The other parameters are given as follows:

\overline{x} = 98.3, s = 11.2, n = 30.

Hence, the bounds of the interval are given by:

\overline{x} - t\frac{s}{\sqrt{n}} = 98.3 - 2.756\frac{11.2}{\sqrt{30}} = 92.664

\overline{x} + t\frac{s}{\sqrt{n}} = 98.3 + 2.756\frac{11.2}{\sqrt{30}} = 103.94

Hence option c is correct.

More can be learned about the t-distribution at brainly.com/question/16162795

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Answer: d=7.5

Step-by-step explanation: 5.5=−2+d                                                                     d−2+2=5.5+2                                                                                                             d=7.5                  

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2 years ago
Find the nth term of this 5 7 9 11 13
NemiM [27]
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4 0
3 years ago
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Two cars start from the same point driving in opposite directions. Both cars drive 6miles. One car stops, the other car makes a
dimaraw [331]

Answer:

  • <u>14.4 mile</u>²

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2. When one car stops and the other car makes a 90° left-hand turn and drive 8 miles, you can model the situation with a right triangle, where one leg is 12 miles, the other leg is 8 miles, and the hypotenuse is the distance that separates the cars.

Hence, you must use Pythagoras to find that distance.

3. Pythagoras

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  • hypotenuse = (12 mile)² + (8 mile)² = 144 mile² + 64 mile² = 208 mile²

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Kate is making pizza she put 8 ounces of cheese on each pizza if she has 4 20ounce packages of cheese how many pieces can she ma
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Step-by-step explanation:


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mars1129 [50]

The sum of squares of numbers is: 13

Step-by-step explanation:

Let x and y be two numbers

Then,

Difference of the squares of the numbers will be:

x^2-y^2

Product will be:

xy

Given identity is:

(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2

Given values are:

Difference of the squares of the numbers=x^2-y^2=5

Product of numbers = xy = 6

Putting the values in the identity

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As we have to only find x^2+y^2

Taking square root on both sides

\sqrt{(x^2+y^2)^2}=\sqrt{169}\\x^2+y^2=13

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Keywords: Identities

Learn more about identities at:

  • brainly.com/question/8902155
  • brainly.com/question/8955867

#LearnwithBrainly

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