Final answer:
To find the probability that the mean IQ of people in the sample is greater than 101, you can use the Central Limit Theorem. The probability is approximately 0.3565, or 35.65%.
Step-by-step explanation:
To find the probability that the mean IQ of people in the sample is greater than 101, we can use the Central Limit Theorem.
The mean IQ of the sample will be approximately normally distributed with a mean of 100 and a standard deviation of the population standard deviation divided by the square root of the sample size.
In this case, the population standard deviation is 15 and the sample size is n, which is not specified.
If we assume a sample size of 30 (a common choice), the standard deviation of the sample mean would be 15/sqrt(30) = 15/5.48 ≈ 2.74.
To find the probability that the mean IQ of the sample is greater than 101, we can convert this to a z-score using the formula Z = (X - μ) / σ, where X is the value we are interested in, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get Z = (101 - 100) / 2.74 ≈ 0.36. We can then look up the z-score in a standard normal distribution table or use a calculator to find the corresponding probability.
For example, using a calculator, we can find that the probability of Z > 0.36 is approximately 0.3565.
Therefore, the probability that the mean IQ of people in the sample is greater than 101 is approximately 0.3565, or 35.65%.