The mean income of firms in the industry for a year is 95 million dollars and a standard deviation of 11 million dollars.
Income for the industry are distributed normally.
We have to find the probability that a randomly selected firm will earn less than 101 million dollars.
Now, let X be the random variable denoting the income of a randomly selected firm in millions of dollars, then X follows normal with mean 95 and standard deviation of 11.
So, we can say that, Z=(X-95)/11 follows standard normal with mean 0 and standard deviation of 1.
We have to find
Where, phi is the distribution function of the standard normal variate.
From the standard normal table, this becomes
The answer is
The approximate probability that a randomly selected firm will earn less than 101 million dollars, is 0.7073.
Suppose the mean income of firms in the industry for a year is 95 million dollars...
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