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sukhopar [10]
3 years ago
11

Which linear inequality is represented by the graph?

Mathematics
1 answer:
omeli [17]3 years ago
7 0

Answer:

Second answer is the correct answer

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The average production cost for major movies is 57 million dollars and the standard deviation is 22 million dollars. Assume the
Degger [83]

Using the normal distribution, we have that:

  • The distribution of X is X \approx (57,22).
  • The distribution of \mathbf{\bar{X}} is \bar{X} \approx (57, 5.3358).
  • 0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.
  • 0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

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

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem, the parameters are given as follows:

\mu = 57, \sigma = 22, n = 17, s = \frac{22}{\sqrt{17}} = 5.3358

Hence:

  • The distribution of X is X \approx (57,22).
  • The distribution of \mathbf{\bar{X}} is \bar{X} \approx (57, 5.3358).

The probabilities are the <u>p-value of Z when X = 58 subtracted by the p-value of Z when X = 55</u>, hence, for a single movie:

X = 58:

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

Z = \frac{58 - 57}{22}

Z = 0.05.

Z = 0.05 has a p-value of 0.5199.

X = 55:

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

Z = \frac{55 - 57}{22}

Z = -0.1.

Z = -0.1 has a p-value of 0.4602.

0.5199 - 0.4602 = 0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.

For the sample of 17 movies, we have that:

X = 58:

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

Z = \frac{58 - 57}{5.3358}

Z = 0.19.

Z = 0.19 has a p-value of 0.5753.

X = 55:

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

Z = \frac{55 - 57}{5.3358}

Z = -0.38.

Z = -0.38 has a p-value of 0.3520.

0.5753 - 0.3520 = 0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

8 0
2 years ago
What is the area of a rectangles with the side lengths 5 inches and 1/3 inches? ​
sveticcg [70]

Answer:

area of a rectangle is length multiplied by breath, which is the multiplication of 5 an 1/3

3 0
3 years ago
Help me I pay you guys
Eva8 [605]

Answer:

20 degree angle

Step-by-step explanation:

8 0
2 years ago
What is 2 + 10? pls help!!!!!!
Jlenok [28]
12 because if you take 2 and add it to 10 you get 12
3 0
3 years ago
Read 2 more answers
A cylinder shaped jar has a radius of 2 cm and a height of 6cm. What’s the volume of the jar?
max2010maxim [7]
The formula to find the volume of a cylinder is v= hㅠr*2, so you can sub the measurements into the formula.

V = (6)ㅠ(2)*2

V = 6ㅠ4

V= 75.4 (approx)
7 0
3 years ago
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