A company pays its employees an average wage of $14.90 an hour with a standard deviation of $1.50. If the wages are approximately normally distributed and paid to the nearest cent, the highest 7% of the employees hourly wages is greater than what amount? Report your code, as well as your final answer (2 decimals).

And if we solve for a we got

So the value of height that separates the bottom 93% of data from the top 3% is 17.12.  

Explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the wages per hour of a population, and for this case we know the distribution for X is given by:

Where and

For this part we want to find a value a, such that we satisfy this condition:

  (a)

  (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.93 of the area on the left and 0.07 of the area on the right it's z=1.478. On this case P(Z<1.478)=0.93 and P(z>1.478)=0.07

If we use condition (b) from previous we have this:

But we know which value of z satisfy the previous equation so then we can do this:

And if we solve for a we got

So the value of height that separates the bottom 93% of data from the top 3% is 17.12.  

answer; hazards;

whole quiz

1. the sum of all activities involved in getting high-quality products into the marketplace

2.operations

3. the principle of looking at the supply chain as a whole in order to improve the overall flow through the system.

4. produced; performed

5. activities producing tangible products, such as radios, newspapers, buses, and textbooks.

6. activities producing intangible and tangible products, such as entertainment, transportation, and education.

7.   customer focus

8. analyzing a competitor's products to identify desirable improvements

9. the systematic direction and control of the processes that transform resources into finished projects that create value for and provide benefits to consumers.

10. operation management.

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