four friends attended a painting class together. They each paid for a ticket and $15 for food. At the end of the night, the tota
1 answer:
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Answer:
Quantity = 59 units
Price = $111
Step-by-step explanation:
The Demand function is given by
The Marginal cost is given by
We are asked to find the quantity and price of goods.
Firstly, obtain the Marginal revenue function from the demand function
The Total revenue is given by
The Marginal revenue is the derivative of the Total revenue,
Assuming that the monopolist maximizes profits,
Therefore, the quantity is 59 units.
The price of each good is
Therefore, the price is $111.
Answer:
54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using 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 problem, we have that:
What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches
Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.
Lesser than 207.9.
pvalue of Z when X = 207.9. So
By the Central Limit Theorem
has a pvalue of 0.2743
2*0.2743 = 0.5486
54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches