IQ scores are normally distributed with a mean of 100 and a standard deviation of 15 . Out of a randomly selected 1350 people from the population, how many of them would have an IQ between 95 and 123 , to the nearest whole number?

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Identify Mean and Standard Deviation: Identify the mean and standard deviation of the IQ scores. Mean (μ) = 100 Standard deviation (σ) = 15Calculate Z-Scores: Calculate the z-scores for the IQ scores of 95 and 123. The z-score formula is z = (X - μ) / σ, where X is the value from the data set. For IQ = 95: z = (95 - 100) / 15 = -5 / 15 = -1/3 ≈ -0.33 For IQ = 123: z = (123 - 100) / 15 = 23 / 15 ≈ 1.53Find Area Under the Curve: Use the standard normal distribution table or a calculator to find the area under the curve between the z-scores of -0.33 and 1.53. The area under the curve from the mean to z = -0.33 is approximately 0.3707. The area under the curve from the mean to z = 1.53 is approximately 0.9370.Calculate Area Between Z-Scores: Calculate the area between the two z-scores by subtracting the area from the mean to z = -0.33 from the area from the mean to z = 1.53. Area between z = -0.33 and z = 1.53 = 0.9370 - 0.3707 = 0.5663Find Number of People: Multiply the area by the total number of people to find the number of people with an IQ between 95 and 123. Number of people = Total population * Area between z-scores Number of people = 1350 * 0.5663 ≈ 764.805Round to Nearest Whole Number: Round the result to the nearest whole number, as we cannot have a fraction of a person. Number of people ≈ 765

IQ scores are normally distributed with a mean of $100$ and a standard deviation of $15$ . Out of a randomly selected $1350$ people from the population, how many of them would have an IQ between $95$ and $123$ , to the nearest whole number?

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IQ scores are normally distributed with a mean of 100100100 and a standard deviation of 151515 . Out of a randomly selected 135013501350 people from the population, how many of them would have an IQ between 959595 and 123123123 , to the nearest whole number?

IQ scores are normally distributed with a mean of $100$ and a standard deviation of $15$ . Out of a randomly selected $1350$ people from the population, how many of them would have an IQ between $95$ and $123$ , to the nearest whole number?