The price of a movie ticket in a given year can be modeled by the regression equation y = 6.94(1.02x), where y is the ticket pri
2 answers:
Answer:
11.38.
Step-by-step explanation:
Given :The price of a movie ticket in a given year can be modeled by the regression equation , where y is the ticket price and x is the year.
To Find: . To the nearest cent, which is the best prediction of the price of a ticket in year 25?
Solution:
Where y is the ticket price and x is the year.
Now we are supposed to find which is the best prediction of the price of a ticket in year 25
Substitute x = 25 in the given equation.
Thus the best prediction of the price of a ticket in year 25 is 11.38.
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Answer:
220 grams.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
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 pvalue, 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 and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
If you pick 22 fruits at random, then 3% of the time, their mean weight will be greater than how many grams?
We have to find the 100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So X when Z = 1.88.
By the Central Limit Theorem
The answer is 220 grams.