Answer:
The measure of x is
Step-by-step explanation:
we know that
The formula to calculate the sum of the internal angles of a polygon is equal to
where
n is the number of sides
In this problem we have
substitute
Find the measure of each internal angle
Divide the sum of the internal angles by the number of sides
The value of x is half the measure of internal angle
so
Using the normal distribution, we have that:
The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
In this problem, the parameters are given as follows:
Hence:
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 = 0.05.
Z = 0.05 has a p-value of 0.5199.
X = 55:
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 = 0.19.
Z = 0.19 has a p-value of 0.5753.
X = 55:
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
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