For a normal population with a mean of µ = 80 and a standard deviation of σ = 10,what is the probability of obtaining a sample mean greater than M = 75 for a sample of n = 25 scores?
A)p = 0.0062
B)p = 0.9938
C)p = 0.3085
D)p = 0.6915

Question

For a normal population with a mean of µ = 80 and a standard deviation of σ = 10,what is the probability of obtaining a sample mean greater than M = 75 for a sample of n = 25 scores?​
A)p = 0.0062​
B)​p = 0.9938
C)​p = 0.3085
D)​p = 0.6915

Quizplus · Accepted Answer

To find the probability of obtaining a sample mean greater than 75, we use the Z-score formula for a sample mean: Z = (M - µ) / (σ/√n), where M is the sample mean, µ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the values: Z = (75 - 80) / (10/√25) = -5 / (10/5) = -5 / 2 = -2.5. Looking up the Z-score of -2.5 in the Z-table gives the probability of obtaining a score less than 75. To find the probability of obtaining a score greater than 75, we subtract this value from 1. The Z-table value for -2.5 is approximately 0.0062, so 1 - 0.0062 = 0.9938, indicating a high probability of obtaining a sample mean greater than 75.

For a Normal Population with a Mean of µ =