Question

Example: For IQs, what proportion of all possible samples of n = 50 have means of 103 or higher (and we know IQ has 15 as SD)?

A) 0.8413
B) 0.1587
C) 0.9772
D) 0.0228

Answer 1

To find the proportion of all possible samples of n = 50 with means of 103 or higher, we can use the sampling distribution of sample means. Since the population standard deviation is known (15), we can use the normal distribution for our calculations. The proportion of all possible samples with means of 103 or higher is 0.0228.

Step-by-step explanation:

To find the proportion of all possible samples of n = 50 with means of 103 or higher, we can use the sampling distribution of sample means. Since the population standard deviation is known (15), we can use the normal distribution for our calculations.

1. First, we need to calculate the standard error of the mean using the formula: standard deviation / sqrt(sample size). In this case, the standard error is 15 / sqrt(50).
2. Next, we convert the mean of 103 to a z-score using the formula: z = (sample mean - population mean) / standard error. The z-score for 103 is (103 - 100) / (15 / sqrt(50)).
3. Finally, we look up the proportion in the standard normal distribution table for a z-score of the calculated value. The answer is option D) 0.0228.