Alex is running a recycling business. The weight of collected used Iron in a day is a variable, X, which is normally distributed with mean 203 kg and standard deviation 40 kg. If the cost to recycle each kg of used Iron is $15 and the other cost for running the recycling business per day is $2300, the total expense per day, T, is given by T = 15X + 2300.(a) Find mean and the standard deviation of T.(b) There is a 13.8% chance that the total daily expense of the business is more than $K. Find the value of K.(c) Suppose each kg of collected used Iron can be sold for $35 after the recycling. Find the mean, median and the standard deviation of the daily profit of the business.(d) Alex can apply for government allowance if there is more than 10% chance that his recycling business has negative profit in a day. Can he apply for the government allowance? Explain your answer with calculation.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Alex is running a recycling business. The weight of collected used Iron in a day is a variable, X, which is
(a) Find mean and the standard deviation of T.
(b) There is a 13.8% chance that the total daily expense of the business is more than $K. Find the value of K.
(c) Suppose each kg of collected used Iron can be sold for $35 after the recycling. Find the mean,
(d) Alex can apply for government allowance if there is more than 10% chance that his recycling business has negative profit in a day. Can he apply for the government allowance? Explain your answer with calculation.
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