The weekly incomes of shift foreman for a given industry follow a normal probability distribution. With a mean of $1,000 and a standard deviation of $100, what is the z-value for the income (called X) of a foreman who earns $1100 per week? For a foreman who earns $900 per week? In words, what do your results indicate?

Question

Business

Valentin Sosa

18 May, 14:25

The weekly incomes of shift foreman for a given industry follow a normal probability distribution. With a mean of $1,000 and a standard deviation of $100, what is the z-value for the income (called X) of a foreman who earns $1100 per week? For a foreman who earns $900 per week? In words, what do your results indicate?

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Answers (1)

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Darien Sherman · Answer 1

There is a 0.2419% for a foreman to earn either $1,100 or $900

Explanation:

We calculate the probability of a normal distribution of 0; 1

(X-mean) / deviation = Z

(1,100 - 1,000) / 100 = 100/100 = 1

900 - 1,00/100 = - 100/100 = - 1

Given the zame Z value, we have the same probability of a foreman to earn 1,100 or 900

As we are asked for the foreman salary, wewill calcualte the Z for non cumulative, just the probability of a foreman to earn 1,100 or 900 dollars.

We look into the normal distribution table for the value of z = - 1 or 1

0.002419707 = 0.2419%