In 1983, a microwave oven cost $78. 75. Today, a microwave oven costs $92. 66. If the CPI is 177, what is the relation of the ac
1 answer:
The actual price is $46.73 lower than the expected price.
<h3>What is the Formula for Consumer Price Index?</h3>
CPI=consumer price index in the current period
Ct= expected cost in current period
C₀ =cost in the base period
It is given that
Price in base period ie 1983 C₀= $78.75
The actual cost of the microwave oven = $92.66
Consumer Price Index= 177
So, expected price of microwave oven in the current period
Ct= CPIt * C₀ /100 = 177*78.75/100 = $139.39
Difference between the actual price and expected price = 139.39-92.66=$46.73
Therefore, The actual price is $46.73 lower than the expected price.
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Answer:
0.7780
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.
Population:
We have that
Sample of 12:
What is the probability that the mean cost will be more than $7.00?
This is 1 subtracted by the pvalue of Z when X = 7. So
By the Central Limit Theorem
has a pvalue of 0.222
1 - 0.222 = 0.778
So the answer is 0.7780