Questions: Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 11. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 67 and 133? (b) What percentage of people has an IQ score less than 78 or greater than 122? (c) What percentage of people has an IQ score greater than 127? (a) % (Type an integer or a decimal.) (b) % (Type an integer or a decimal.) (c) % (Type an integer or a decimal.)

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 11. Use the empirical rule to determine the following.
(a) What percentage of people has an IQ score between 67 and 133?
(b) What percentage of people has an IQ score less than 78 or greater than 122?
(c) What percentage of people has an IQ score greater than 127?
(a) % (Type an integer or a decimal.)
(b) % (Type an integer or a decimal.)
(c) % (Type an integer or a decimal.)

Transcript text: Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 11 . Use the empirical rule to deternine the following. (a) What percentage of people has an IQ score between 67 and 133 ? (b) What percentage of people has an IQ score less than 78 or greater than $122 ?$ (c) What percentage of people has an IQ score greater than 127 ? (a) $\square$ $\%$ (Type an integer or a decimal.) (b) $\square$ \% (Type an integer or a decimal.) (c) $\square$ \% (Type an integer or a decimal.)

Solution

Solution Steps

Step 1: Identify the Mean (\mu) and Standard Deviation (\sigma)

The mean ($\mu$) of the IQ scores is 100, and the standard deviation ($\sigma$) is 11.

Step 2: Apply the Empirical Rule or Calculate Specific Percentages

For the IQ score range (67, 133), the percentage of the population within this range is approximately 99.73%.

Final Answer:

The percentage of the population with IQ scores between 67 and 133 is approximately 99.73%.

Step 1: Identify the Mean (\mu) and Standard Deviation (\sigma)

The mean ($\mu$) of the IQ scores is 100, and the standard deviation ($\sigma$) is 11.

Step 2: Apply the Empirical Rule or Calculate Specific Percentages

For the IQ score 78, the percentage of the population below this score is approximately 2.28%, and above this score is approximately 97.72%.

Final Answer:

The percentage of the population with an IQ score below 78 is approximately 2.28%, and above 78 is approximately 97.72%.

Step 1: Identify the Mean (\mu) and Standard Deviation (\sigma)

The mean ($\mu$) of the IQ scores is 100, and the standard deviation ($\sigma$) is 11.

Step 2: Apply the Empirical Rule or Calculate Specific Percentages

For the IQ score 122, the percentage of the population below this score is approximately 97.72%, and above this score is approximately 2.28%.

Final Answer:

The percentage of the population with an IQ score below 122 is approximately 97.72%, and above 122 is approximately 2.28%.

Step 1: Identify the Mean (\mu) and Standard Deviation (\sigma)

The mean ($\mu$) of the IQ scores is 100, and the standard deviation ($\sigma$) is 11.

Step 2: Apply the Empirical Rule or Calculate Specific Percentages

For the IQ score 127, the percentage of the population below this score is approximately 99.29%, and above this score is approximately 0.71%.

Final Answer:

The percentage of the population with an IQ score below 127 is approximately 99.29%, and above 127 is approximately 0.71%.

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