Question

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The percentage of employees who would have iqs between 90and 115 would be ?

Answer 1

To find the percent of employees with IQs between 90 and 115, we standardize the values using the z-score formula and find the area under the normal distribution curve between these two standardized values. The percentage is approximately 67.3%.

To find the percent of employees with IQs between 90 and 115, we need to find the area under the normal distribution curve between these two values.

First, we need to standardize the values using the formula

z = (x - mean) / standard deviation

where x is the given value, mean is 100, and standard deviation is 12.5.

For 90, the standardized value is z = (90 - 100) / 12.5 = -0.8, and for 115, the standardized value is

z = (115 - 100) / 12.5 = 1.2.

We can then use a standard normal distribution table or a calculator to find the area between these two z-scores.

The area under the curve for z = -0.8 is 0.2119, and the area under the curve for z = 1.2 is 0.8849.

To find the percent, we subtract the smaller area from the larger area: 0.8849 - 0.2119 = 0.673.

Therefore, approximately 67.3% of employees would have IQs between 90 and 115.

Question:

A large company employs workers whose IQs are distributed normally with mean 100 and standard deviation 12.5. Management uses this information to assign employees to projects that will be challenging, but not too challenging. What percent of employees would have IQs between 90 and 115?

Answer 2

To find the percentage of employees with IQs between 90 and 115, convert the IQ scores to z-scores and use a standard normal distribution table or calculator to determine the corresponding probabilities. Subtract the probability of the lower z-score from the probability of the higher z-score to get the final percentage.

Step-by-step explanation:

To solve for the percentage of employees who would have IQs between 90 and 115, we can assume that IQ scores follow a normal distribution with a mean (μ) of 100 and a standard deviation (σ) of 15. You can use the z-score formula to convert these IQs to their corresponding z-scores.

For IQ = 90:
Z = (X - μ) / σ = (90 - 100) / 15 = -0.6667
For IQ = 115:
Z = (X - μ) / σ = (115 - 100) / 15 = 1

You would then look up these z-scores on a standard normal distribution table or use a calculator with this functionality to find the probabilities corresponding to each z-score. The percentage of employees with IQ scores between 90 and 115 would be the difference between these two probabilities.